| 1 | program sfbasic |
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| 2 | c============================================================ |
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| 3 | c Combine evolution of w = h+z and h for shallow flows |
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| 4 | c============================================================ |
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| 5 | |
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| 6 | implicit none |
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| 7 | |
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| 8 | integer md,nxmax,nxd, mn |
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| 9 | |
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| 10 | parameter (md=3, nxmax=5000, nxd=nxmax+2*md, mn=2) |
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| 11 | real*8 h(nxd), uh(nxd), w(nxd) |
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| 12 | real*8 z(nxd),z2(nxd) |
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| 13 | real*8 x(nxd),x2(nxd) |
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| 14 | |
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| 15 | integer terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
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| 16 | common /setup/ terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
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| 17 | |
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| 18 | integer nlow,nhigh,nx,nxx,dn,version,isteps |
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| 19 | common /ivariables/ nlow,nhigh,nx,nxx,version,isteps |
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| 20 | |
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| 21 | real*8 toll,cfl,theta |
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| 22 | real*8 g,hf,dx,dt,dtmax |
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| 23 | real*8 Tout,tf,tc,uhf |
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| 24 | real*8 K,limith,length |
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| 25 | real*8 manning,hl,hr,zb |
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| 26 | common /rvariables/ toll,cfl,theta, |
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| 27 | . g,hf,dx,dt,dtmax, |
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| 28 | . Tout,tf,tc,uhf, |
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| 29 | . K,limith,length, |
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| 30 | . manning,hl,hr |
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| 31 | |
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| 32 | integer io, i |
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| 33 | |
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| 34 | call util_open_files |
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| 35 | |
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| 36 | open(1,file='MacDonald.bed') |
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| 37 | c |
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| 38 | c Parameters |
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| 39 | c |
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| 40 | nx = 101 |
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| 41 | dtmax = 1.0d0 |
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| 42 | Tout = 1.0d0 |
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| 43 | tf = 200.0d0 |
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| 44 | length = 1000.0d0 |
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| 45 | |
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| 46 | nlow = md+2 |
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| 47 | nhigh = md+nx |
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| 48 | nxx = nx+2*md |
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| 49 | |
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| 50 | limith = 1 |
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| 51 | dx = 10.d0 |
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| 52 | K = 0.0d0 |
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| 53 | |
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| 54 | if (nx.gt.nxmax) write(*,*)'nx too large' |
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| 55 | toll = 1.0d-10 |
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| 56 | cfl = 0.01d0 |
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| 57 | theta = 1.2d0 |
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| 58 | version = 10 |
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| 59 | g = 9.81d0 |
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| 60 | hl = 5.d0 |
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| 61 | hr = 0.d0 |
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| 62 | tc = 0.d0 |
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| 63 | |
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| 64 | c |
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| 65 | c ---- Setup Terrain, Boundary Values and Initial Values |
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| 66 | c |
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| 67 | |
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| 68 | c ---- Non-uniform terrain from MacDonald |
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| 69 | do i = 1,nxx |
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| 70 | read(1,*)x2(i),z2(i) |
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| 71 | z2(i) = z2(i)*5.d0 |
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| 72 | x(i) = x2(i) - dx/2.d0 |
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| 73 | end do |
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| 74 | do i = 2,nxx |
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| 75 | z(i) = (z2(i-1)+z2(i))/2.d0 |
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| 76 | end do |
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| 77 | z(1) = (3.d0*z2(1) - z2(2))/2.d0 |
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| 78 | z(nxx) = (3.d0*z2(nxx-1) - z2(nxx-2))/2.d0 |
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| 79 | |
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| 80 | call boundary_apply(x,h,uh,z) |
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| 81 | |
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| 82 | c ---- Rectangular pulse initial condition |
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| 83 | do i = md+1, nx+md |
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| 84 | if (x(i).lt.100.d0.or.x(i).gt.200.d0) then |
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| 85 | h(i) = hr |
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| 86 | else |
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| 87 | h(i) = hl |
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| 88 | endif |
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| 89 | uh(i) = 0.0d0 |
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| 90 | end do |
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| 91 | c |
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| 92 | c ---- Setup for Time looping |
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| 93 | c |
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| 94 | isteps = 0 |
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| 95 | tc = 0.0d0 |
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| 96 | call util_dump_solution(h,uh,z) |
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| 97 | c |
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| 98 | c ---- Evolve |
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| 99 | c |
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| 100 | call evolver_euler(x,h,uh,z,z2) |
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| 101 | c |
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| 102 | c ---- Close down |
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| 103 | c |
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| 104 | write(15,*)isteps,nxx,version |
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| 105 | do i=1,nxx |
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| 106 | write(16,*) x(i) |
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| 107 | enddo |
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| 108 | |
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| 109 | do i=5,nxx-3 |
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| 110 | write(25,*) x(i) |
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| 111 | enddo |
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| 112 | |
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| 113 | call util_close_files |
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| 114 | |
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| 115 | stop |
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| 116 | end |
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| 117 | c=========================================================== |
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| 118 | c Shallow Water Flux |
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| 119 | c=========================================================== |
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| 120 | subroutine flux_huh(f1,f2,h0,uh0,em_x,l1,l2,g,toll) |
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| 121 | implicit none |
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| 122 | |
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| 123 | real*8 f1,f2,h0,uh0,z,l1,l2 |
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| 124 | real*8 em_x,g,toll |
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| 125 | |
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| 126 | real*8 u,cvel,h,uh,w |
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| 127 | integer i |
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| 128 | |
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| 129 | c----------------------------------- |
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| 130 | |
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| 131 | if(em_x.lt.1.0d-15) then |
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| 132 | em_x = 1.d-15 |
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| 133 | endif |
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| 134 | |
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| 135 | uh = uh0 |
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| 136 | h = h0 |
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| 137 | |
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| 138 | if(h.le.toll)then |
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| 139 | u = 0.d0 |
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| 140 | h = 0.0d0 |
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| 141 | uh = 0.0d0 |
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| 142 | else |
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| 143 | u = uh/h |
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| 144 | endif |
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| 145 | |
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| 146 | cvel = dsqrt( g*h ) |
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| 147 | l1 = u - cvel |
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| 148 | l2 = u + cvel |
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| 149 | em_x = dmax1( em_x, dabs(u) + cvel ) |
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| 150 | f1 = uh |
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| 151 | f2 = uh*u + 0.5d0*g*h**2 |
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| 152 | |
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| 153 | return |
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| 154 | end |
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| 155 | c=========================================================== |
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| 156 | c Shallow Water Flux |
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| 157 | c=========================================================== |
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| 158 | subroutine flux_huh_old(f1,f2,h0,uh0,z,em_x,l1,l2,g,toll) |
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| 159 | implicit none |
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| 160 | |
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| 161 | real*8 f1,f2,h0,uh0,z,l1,l2 |
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| 162 | real*8 em_x,g,toll |
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| 163 | |
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| 164 | real*8 u,cvel,h,uh,w |
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| 165 | integer i |
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| 166 | |
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| 167 | c----------------------------------- |
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| 168 | |
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| 169 | if(em_x.lt.1.0d-15) then |
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| 170 | em_x = 1.d-15 |
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| 171 | endif |
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| 172 | |
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| 173 | w = h0+z |
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| 174 | uh = uh0 |
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| 175 | h = h0 |
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| 176 | |
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| 177 | if(h.le.toll)then |
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| 178 | u = 0.d0 |
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| 179 | h = 0.0d0 |
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| 180 | uh = 0.0d0 |
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| 181 | else |
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| 182 | u = uh / h |
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| 183 | endif |
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| 184 | if (abs(u).gt.1.0d1) then |
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| 185 | u = dsign(1.0d0,u)*1.0d3 |
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| 186 | uh = u*h |
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| 187 | end if |
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| 188 | cvel = dsqrt( g*h ) |
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| 189 | l1 = u - cvel |
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| 190 | l2 = u + cvel |
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| 191 | em_x = dmax1( em_x, dabs(u) + cvel ) |
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| 192 | f1 = uh |
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| 193 | f2 = uh*u + 0.5d0*g*h**2 |
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| 194 | |
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| 195 | return |
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| 196 | end |
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| 197 | c=========================================================== |
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| 198 | c Shallow Water Flux using h+z and uh variables |
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| 199 | c=========================================================== |
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| 200 | subroutine flux_wuh(f1,f2,w0,uh0,z,em_x,l1,l2,g,toll) |
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| 201 | implicit none |
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| 202 | |
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| 203 | real*8 f1,f2,w0,uh0,z |
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| 204 | real*8 g,toll |
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| 205 | |
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| 206 | real*8 h,u,cvel,uh,w,l1,l2,em_x |
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| 207 | integer i |
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| 208 | |
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| 209 | c----------------------------------- |
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| 210 | |
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| 211 | if(em_x.lt.1.0d-15) then |
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| 212 | em_x = 1.d-15 |
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| 213 | endif |
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| 214 | |
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| 215 | w = w0 |
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| 216 | uh = uh0 |
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| 217 | |
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| 218 | h = w - z |
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| 219 | if(h.le.toll)then |
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| 220 | u = 0.d0 |
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| 221 | h = 0.0d0 |
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| 222 | uh = 0.0d0 |
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| 223 | else |
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| 224 | u = uh / h |
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| 225 | endif |
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| 226 | if (abs(u).gt.1.0d3) then |
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| 227 | u = dsign(1.0d0,u)*1.0d3 |
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| 228 | uh = u*h |
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| 229 | end if |
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| 230 | cvel = dsqrt( g*h ) |
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| 231 | l1 = u - cvel |
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| 232 | l2 = u + cvel |
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| 233 | em_x = dmax1( em_x, dabs(u) + cvel ) |
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| 234 | f1 = uh |
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| 235 | f2 = uh*u + 0.5d0*g*h**2 |
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| 236 | |
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| 237 | return |
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| 238 | end |
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| 239 | c=============================================================== |
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| 240 | c array limiter |
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| 241 | c=============================================================== |
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| 242 | subroutine array_limit_h(h,uh,z2,z,uh_l,uh_r,h_l,h_r,h_2) |
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| 243 | |
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| 244 | implicit none |
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| 245 | integer md,nxmax,nxd, mn |
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| 246 | parameter (md=3, nxmax=5000, nxd=nxmax+2*md, mn=2) |
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| 247 | real*8 h(nxd), uh(nxd), w(nxd) |
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| 248 | real*8 z(nxd),z2(nxd) |
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| 249 | real*8 x(nxd),x2(nxd) |
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| 250 | |
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| 251 | integer terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
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| 252 | common /setup/ terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
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| 253 | |
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| 254 | integer nlow,nhigh,nx,nxx,dn,version,isteps |
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| 255 | common /ivariables/ nlow,nhigh,nx,nxx,version,isteps |
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| 256 | |
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| 257 | real*8 toll,cfl,theta |
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| 258 | real*8 g,hf,dx,dt,dtmax |
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| 259 | real*8 Tout,tf,tc,uhf |
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| 260 | real*8 K,limith,length |
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| 261 | real*8 manning,hl,hr |
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| 262 | common /rvariables/ toll,cfl,theta, |
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| 263 | . g,hf,dx,dt,dtmax, |
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| 264 | . Tout,tf,tc,uhf, |
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| 265 | . K,limith,length, |
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| 266 | . manning,hl,hr |
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| 267 | |
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| 268 | real*8 h_2(nxd) |
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| 269 | real*8 h_l(nxd),h_r(nxd) |
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| 270 | real*8 h1_l(nxd), h1_r(nxd) |
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| 271 | real*8 uh_l(nxd), uh_r(nxd) |
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| 272 | |
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| 273 | integer sslope(nxd) |
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| 274 | real*8 xmin,xmic,xminmod,a,b,c,t |
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| 275 | |
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| 276 | xmin(a,b) = 0.5d0*(dsign(1.d0,a)+dsign(1.d0,b))* |
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| 277 | . dmin1(dabs(a),dabs(b)) |
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| 278 | xmic(t,a,b) = xmin(t*xmin(a,b), 0.5d0*(a+b) ) |
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| 279 | xminmod(a,b,c) = xmin(a,xmin(b,c)) |
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| 280 | |
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| 281 | |
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| 282 | integer i |
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| 283 | real*8 dh, hmax, hmin , tt, cc |
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| 284 | real*8 w0,w1,w2,d0h,d0w,d1h,d1w,d2h,d2w,ddh,ddw |
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| 285 | real*8 h0,h1,h2,hz |
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| 286 | real*8 ss0,ss1,ss |
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| 287 | real*8 dz0,dz1,dz2 |
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| 288 | real*8 hx1,hx2,h_x |
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| 289 | real*8 froud,d1,d2 |
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| 290 | real*8 gh3,uh2,duh, w_x,dz |
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| 291 | |
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| 292 | c------------------------------------ |
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| 293 | g = 9.81d0 |
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| 294 | cc = 0.1d0 |
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| 295 | ss0 = 0.01d0 |
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| 296 | ss1 = 0.01d0 |
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| 297 | |
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| 298 | do i=md,nx+md+2 |
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| 299 | |
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| 300 | h_2(i) = h(i) |
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| 301 | h0 = h(i-1) |
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| 302 | h1 = h(i) |
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| 303 | h2 = h(i+1) |
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| 304 | |
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| 305 | dz0 = abs(z2(i-1)-z2(i-2)) |
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| 306 | dz1 = abs(z2(i) -z2(i-1)) |
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| 307 | dz2 = abs(z2(i+1)-z2(i) ) |
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| 308 | |
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| 309 | w0 = h0 + z(i-1) |
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| 310 | w1 = h1 + z(i) |
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| 311 | w2 = h2 + z(i+1) |
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| 312 | |
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| 313 | d1w = w1 - w0 |
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| 314 | d2w = w2 - w1 |
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| 315 | dz = (z2(i) - z2(i-1)) |
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| 316 | |
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| 317 | c ------- W = H+Z |
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| 318 | h_x = xmin( d1w, d2w) - dz |
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| 319 | |
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| 320 | c ------- Return the left and right values of h in an interval |
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| 321 | h_l(i) = h(i) - 0.5d0*h_x |
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| 322 | h_r(i) = h(i) + 0.5d0*h_x |
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| 323 | |
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| 324 | c ------- Test for h_l or h_r negative |
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| 325 | hmin = dmin1(h0,h1,h2) |
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| 326 | if ( h_l(i) .le. hmin ) then |
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| 327 | h_l(i) = hmin |
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| 328 | h_r(i) = h(i) + (h(i) - h_l(i)) |
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| 329 | elseif ( h_r(i) .le. hmin ) then |
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| 330 | h_r(i) = hmin |
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| 331 | h_l(i) = h(i) + (h(i) - h_r(i)) |
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| 332 | endif |
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| 333 | enddo |
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| 334 | c |
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| 335 | c ---- Enforce a minimum height |
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| 336 | c |
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| 337 | do i=md,nx+md+2 |
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| 338 | hmax = dmax1(h_l(i),h_r(i)) |
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| 339 | if (hmax .lt. 1.0d-3 ) then |
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| 340 | h_r(i) = 0.0d0 |
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| 341 | uh_r(i) = 0.0d0 |
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| 342 | h_l(i) = 0.0d0 |
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| 343 | uh_l(i) = 0.0d0 |
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| 344 | h(i) = 0.0d0 |
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| 345 | uh(i) = 0.0d0 |
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| 346 | endif |
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| 347 | enddo |
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| 348 | c |
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| 349 | c ---- Try for a flat subinterval |
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| 350 | c |
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| 351 | do i=md,nx+md+2 |
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| 352 | hmax = dmax1(h_l(i),h_r(i)) |
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| 353 | dz = (z2(i) - z2(i-1)) |
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| 354 | |
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| 355 | if (h_l(i) .lt. 0.01d0*h_r(i) ) then |
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| 356 | h_r(i) = sqrt(abs(2.0d0*dz*h(i))) |
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| 357 | endif |
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| 358 | |
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| 359 | if (h_r(i) .lt. 0.01d0*h_l(i) ) then |
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| 360 | h_l(i) = sqrt(abs(2.0d0*dz*h(i))) |
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| 361 | endif |
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| 362 | enddo |
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| 363 | |
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| 364 | return |
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| 365 | end |
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| 366 | c=============================================================== |
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| 367 | c array limiter |
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| 368 | c=============================================================== |
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| 369 | subroutine array_limit(u,u_l,u_r) |
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| 370 | |
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| 371 | implicit none |
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| 372 | integer md,nxmax,nxd, mn |
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| 373 | parameter (md=3, nxmax=5000, nxd=nxmax+2*md, mn=2) |
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| 374 | real*8 h(nxd), uh(nxd), w(nxd) |
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| 375 | real*8 z(nxd),z2(nxd) |
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| 376 | real*8 x(nxd),x2(nxd) |
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| 377 | |
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| 378 | integer terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
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| 379 | common /setup/ terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
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| 380 | |
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| 381 | integer nlow,nhigh,nx,nxx,dn,version,isteps |
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| 382 | common /ivariables/ nlow,nhigh,nx,nxx,version,isteps |
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| 383 | |
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| 384 | real*8 toll,cfl,theta |
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| 385 | real*8 g,hf,dx,dt,dtmax |
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| 386 | real*8 Tout,tf,tc,uhf |
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| 387 | real*8 K,limith,length |
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| 388 | real*8 manning,hl,hr |
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| 389 | common /rvariables/ toll,cfl,theta, |
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| 390 | . g,hf,dx,dt,dtmax, |
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| 391 | . Tout,tf,tc,uhf, |
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| 392 | . K,limith,length, |
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| 393 | . manning,hl,hr |
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| 394 | |
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| 395 | real*8 u(nxd), u_l(nxd),u_r(nxd) |
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| 396 | real*8 u_x,d1,d2,d0,ux1 |
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| 397 | real*8 u1_l(nxd),u1_r(nxd) |
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| 398 | integer i |
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| 399 | |
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| 400 | real*8 a,b,t,xmin,xmic |
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| 401 | |
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| 402 | xmin(a,b) = 0.5d0*(dsign(1.d0,a)+dsign(1.d0,b))* |
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| 403 | . dmin1(dabs(a),dabs(b)) |
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| 404 | xmic(t,a,b) = xmin(t*xmin(a,b), 0.5d0*(a+b) ) |
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| 405 | |
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| 406 | c------------------------------------ |
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| 407 | |
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| 408 | do i=md,nx+md+2 |
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| 409 | d1 = u(i) - u(i-1) |
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| 410 | d2 = u(i+1) - u(i) |
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| 411 | u_x = xmic( theta, d1, d2 ) |
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| 412 | u_l(i) = u(i) - 0.5d0*u_x |
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| 413 | u_r(i) = u(i) + 0.5d0*u_x |
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| 414 | enddo |
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| 415 | |
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| 416 | return |
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| 417 | end |
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| 418 | c=========================================================== |
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| 419 | c Output Routine |
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| 420 | c=========================================================== |
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| 421 | subroutine util_dump_solution(h,uh,z) |
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| 422 | |
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| 423 | implicit none |
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| 424 | integer md,nxmax,nxd, mn |
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| 425 | parameter (md=3, nxmax=5000, nxd=nxmax+2*md, mn=2) |
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| 426 | real*8 h(nxd), uh(nxd), w(nxd) |
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| 427 | real*8 z(nxd),z2(nxd) |
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| 428 | real*8 x(nxd),x2(nxd) |
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| 429 | |
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| 430 | integer terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
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| 431 | common /setup/ terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
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| 432 | |
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| 433 | integer nlow,nhigh,nx,nxx,dn,version,isteps |
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| 434 | common /ivariables/ nlow,nhigh,nx,nxx,version,isteps |
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| 435 | |
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| 436 | real*8 toll,cfl,theta |
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| 437 | real*8 g,hf,dx,dt,dtmax |
|---|
| 438 | real*8 Tout,tf,tc,uhf |
|---|
| 439 | real*8 K,limith,length |
|---|
| 440 | real*8 manning,hl,hr |
|---|
| 441 | common /rvariables/ toll,cfl,theta, |
|---|
| 442 | . g,hf,dx,dt,dtmax, |
|---|
| 443 | . Tout,tf,tc,uhf, |
|---|
| 444 | . K,limith,length, |
|---|
| 445 | . manning,hl,hr |
|---|
| 446 | |
|---|
| 447 | integer ii,i |
|---|
| 448 | |
|---|
| 449 | write(12,*)tc |
|---|
| 450 | |
|---|
| 451 | isteps = isteps + 1 |
|---|
| 452 | write(*,*)isteps, tc |
|---|
| 453 | |
|---|
| 454 | do i = 1, nx+2*md |
|---|
| 455 | c------ Dump h |
|---|
| 456 | write(13,200)sngl(h(i)) |
|---|
| 457 | c------ Dump uh |
|---|
| 458 | write(14,200)sngl(uh(i)) |
|---|
| 459 | c------ Dump w |
|---|
| 460 | write(11,200)sngl(h(i)+z(i)) |
|---|
| 461 | 200 format(e20.8) |
|---|
| 462 | end do |
|---|
| 463 | |
|---|
| 464 | return |
|---|
| 465 | end |
|---|
| 466 | c=============================================================== |
|---|
| 467 | c The evolver using euler's method |
|---|
| 468 | c=============================================================== |
|---|
| 469 | subroutine evolver_euler(x,h,uh,z,z2) |
|---|
| 470 | |
|---|
| 471 | implicit none |
|---|
| 472 | integer md,nxmax,nxd, mn |
|---|
| 473 | parameter (md=3, nxmax=5000, nxd=nxmax+2*md, mn=2) |
|---|
| 474 | real*8 h(nxd), uh(nxd), w(nxd) |
|---|
| 475 | real*8 z(nxd),z2(nxd) |
|---|
| 476 | real*8 x(nxd),x2(nxd) |
|---|
| 477 | |
|---|
| 478 | integer terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
|---|
| 479 | c common /setup/ terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
|---|
| 480 | |
|---|
| 481 | integer nlow,nhigh,nx,nxx,dn,version,isteps |
|---|
| 482 | common /ivariables/ nlow,nhigh,nx,nxx,version,isteps |
|---|
| 483 | |
|---|
| 484 | real*8 toll,cfl,theta |
|---|
| 485 | real*8 g,hf,dx,dt,dtmax |
|---|
| 486 | real*8 Tout,tf,tc,uhf |
|---|
| 487 | real*8 K,limith,length |
|---|
| 488 | real*8 manning,hl,hr |
|---|
| 489 | common /rvariables/ toll,cfl,theta, |
|---|
| 490 | . g,hf,dx,dt,dtmax, |
|---|
| 491 | . Tout,tf,tc,uhf, |
|---|
| 492 | . K,limith,length, |
|---|
| 493 | . manning,hl,hr |
|---|
| 494 | |
|---|
| 495 | real*8 h_new(nxd),uh_new(nxd) |
|---|
| 496 | real*8 h_h(nxd),uh_h(nxd) |
|---|
| 497 | real*8 h_h_x(nxd),uh_h_x(nxd) |
|---|
| 498 | real*8 h_x(nxd), uh_x(nxd) |
|---|
| 499 | real*8 f_h(nxd), f_uh(nxd) |
|---|
| 500 | real*8 f_h_l(nxd), f_uh_l(nxd) |
|---|
| 501 | real*8 f_h_r(nxd), f_uh_r(nxd) |
|---|
| 502 | real*8 z_l(nxd),z_r(nxd) |
|---|
| 503 | real*8 h_2(nxd), uh_2(nxd) |
|---|
| 504 | |
|---|
| 505 | real*8 h_l(nxd), h_r(nxd), uh_l(nxd), uh_r(nxd) |
|---|
| 506 | real*8 z2l, z2r, zl, zr |
|---|
| 507 | |
|---|
| 508 | integer io, i, jj, ipos,ip |
|---|
| 509 | real*8 factor, Ki |
|---|
| 510 | |
|---|
| 511 | integer istop,iout,nt,ii,oi,i2,m |
|---|
| 512 | real*8 a,b,t,Tleft,em_x,dtcdx,dtcdx2,dtcdx3 |
|---|
| 513 | real*8 den, xmt,pre, Tnext, em_old, hh |
|---|
| 514 | real*8 aterm1 ,term1, aterm2 ,term2, aterm3 ,term3 |
|---|
| 515 | |
|---|
| 516 | integer kk |
|---|
| 517 | real*8 umax, umax2, vmin, q1,q2,q3,h1,h2 |
|---|
| 518 | real*8 Kcal,k1,k2,za,zb,pi |
|---|
| 519 | |
|---|
| 520 | real*8 fh_l, fuh_l, fh_r, fuh_r |
|---|
| 521 | real*8 l1_l, l2_l, l1_r, l2_r |
|---|
| 522 | real*8 a_max, a_min, aa, axa |
|---|
| 523 | |
|---|
| 524 | c---------------------------------------------------------- |
|---|
| 525 | c |
|---|
| 526 | pi = 2.d0*dtan(1.d0) |
|---|
| 527 | factor = 1.0d0 |
|---|
| 528 | em_old = 1.0d0 |
|---|
| 529 | tc = 0.d0 |
|---|
| 530 | istop = 0 |
|---|
| 531 | iout = 0 |
|---|
| 532 | nt =0 |
|---|
| 533 | Tleft = dmin1(Tout,tf) |
|---|
| 534 | Tnext = dmin1(Tout,tf) |
|---|
| 535 | dt = dmin1(dtmax,Tleft) |
|---|
| 536 | |
|---|
| 537 | do i=1,nxx |
|---|
| 538 | f_h(i) = 0.0d0 |
|---|
| 539 | f_uh(i) = 0.0d0 |
|---|
| 540 | h_l(i) = h(i) |
|---|
| 541 | h_r(i) = h(i) |
|---|
| 542 | uh_l(i) = uh(i) |
|---|
| 543 | uh_r(i) = uh(i) |
|---|
| 544 | enddo |
|---|
| 545 | |
|---|
| 546 | call boundary_apply(x,h,uh,z) |
|---|
| 547 | call array_limit (uh,uh_l,uh_r) |
|---|
| 548 | call array_limit_h(h,uh,z2,z,uh_l,uh_r,h_l,h_r,h_2) |
|---|
| 549 | |
|---|
| 550 | do i=1,nxx |
|---|
| 551 | if ( h(i) .lt. 0.0d0 ) then |
|---|
| 552 | write(*,*)'i=',i,' h(i) = ',h(i) |
|---|
| 553 | endif |
|---|
| 554 | enddo |
|---|
| 555 | |
|---|
| 556 | c------------------------------------------------------ |
|---|
| 557 | c |
|---|
| 558 | do while (.true.) |
|---|
| 559 | c write(*,*)nt |
|---|
| 560 | nt = nt+1 |
|---|
| 561 | ii = 1 |
|---|
| 562 | |
|---|
| 563 | call boundary_apply(x,h,uh,z) |
|---|
| 564 | |
|---|
| 565 | call array_limit (uh,uh_l,uh_r) |
|---|
| 566 | call array_limit_h(h,uh,z2,z,uh_l,uh_r,h_l,h_r,h_2) |
|---|
| 567 | |
|---|
| 568 | do i=1,nxx |
|---|
| 569 | if ( h(i) .lt. 0.0d0 ) then |
|---|
| 570 | write(*,*)'i=',i,' h(i) = ',h(i),' nt = ',nt |
|---|
| 571 | endif |
|---|
| 572 | enddo |
|---|
| 573 | |
|---|
| 574 | c------------------------- |
|---|
| 575 | c Flux Calculation |
|---|
| 576 | c------------------------- |
|---|
| 577 | call numerical_flux_central(h,uh,z2,z,uh_l,uh_r,h_l,h_r,h_2, |
|---|
| 578 | . f_h,f_uh, em_x) |
|---|
| 579 | |
|---|
| 580 | c----------------------------------------------------- |
|---|
| 581 | c Compute time step size according to the input CFL # |
|---|
| 582 | c----------------------------------------------------- |
|---|
| 583 | 1002 dt = dmin1(factor*cfl*dx/em_x,dtmax,Tout) |
|---|
| 584 | c write(*,*)'dt = ',dt,' factor = ',factor |
|---|
| 585 | if( ( tc + dt ) .ge. Tnext ) then |
|---|
| 586 | dt = (Tnext - tc ) |
|---|
| 587 | iout = 1 |
|---|
| 588 | Tnext = Tnext+Tout |
|---|
| 589 | end if |
|---|
| 590 | if (Tnext.gt.tf ) then |
|---|
| 591 | istop = 1 |
|---|
| 592 | endif |
|---|
| 593 | |
|---|
| 594 | c------------------------------------------------- |
|---|
| 595 | c Compute the values of 'u' at the next time level |
|---|
| 596 | c------------------------------------------------- |
|---|
| 597 | ipos = 0 |
|---|
| 598 | |
|---|
| 599 | do i = md+2, md+nx |
|---|
| 600 | |
|---|
| 601 | h_new(i) = h(i) - dt/dx*( f_h(i) - f_h(i-1) ) |
|---|
| 602 | uh_new(i) = uh(i) - dt/dx*( f_uh(i) - f_uh(i-1)) |
|---|
| 603 | . - dt/dx*g*(z2(i)-z2(i-1))*(h(i)) |
|---|
| 604 | |
|---|
| 605 | if (h_new(i).lt.-1.0d-5) then |
|---|
| 606 | write(*,*)'h_new(',i,') = ',h_new(i) |
|---|
| 607 | ipos=1 |
|---|
| 608 | endif |
|---|
| 609 | |
|---|
| 610 | if (h_new(i).le.0.0d0) then |
|---|
| 611 | h_new(i) = 0.0d0 |
|---|
| 612 | c - my statement |
|---|
| 613 | uh_new(i) = 0.d0 |
|---|
| 614 | endif |
|---|
| 615 | |
|---|
| 616 | end do |
|---|
| 617 | |
|---|
| 618 | if(ipos.eq.1) then |
|---|
| 619 | factor = factor/2.0d0 |
|---|
| 620 | write(*,*)'factor = ',factor |
|---|
| 621 | goto 1002 |
|---|
| 622 | endif |
|---|
| 623 | |
|---|
| 624 | do i = md+2,nx+md |
|---|
| 625 | h(i) = h_new(i) |
|---|
| 626 | uh(i) = uh_new(i) |
|---|
| 627 | enddo |
|---|
| 628 | |
|---|
| 629 | factor = 1.0d0 |
|---|
| 630 | tc = tc + dt |
|---|
| 631 | |
|---|
| 632 | if(iout.eq.1) then |
|---|
| 633 | call util_dump_solution(h,uh,z) |
|---|
| 634 | |
|---|
| 635 | call boundary_apply(x,h,uh,z) |
|---|
| 636 | call array_limit (uh,uh_l,uh_r) |
|---|
| 637 | call array_limit_h(h,uh,z2,z,uh_l,uh_r,h_l,h_r,h_2) |
|---|
| 638 | iout = 0 |
|---|
| 639 | endif |
|---|
| 640 | if(istop.eq.1) go to 1001 |
|---|
| 641 | c |
|---|
| 642 | c End timestep |
|---|
| 643 | c |
|---|
| 644 | end do |
|---|
| 645 | c |
|---|
| 646 | 1001 write(*,*)isteps |
|---|
| 647 | |
|---|
| 648 | return |
|---|
| 649 | |
|---|
| 650 | end |
|---|
| 651 | c=========================================================== |
|---|
| 652 | c Boundary Conditions |
|---|
| 653 | c |
|---|
| 654 | c Naive Boundary Conditions |
|---|
| 655 | c Inflow, or reflective |
|---|
| 656 | c |
|---|
| 657 | c=========================================================== |
|---|
| 658 | subroutine boundary_apply(x,h,uh,z) |
|---|
| 659 | |
|---|
| 660 | implicit none |
|---|
| 661 | integer md,nxmax,nxd, mn |
|---|
| 662 | parameter (md=3, nxmax=5000, nxd=nxmax+2*md, mn=2) |
|---|
| 663 | real*8 h(nxd), uh(nxd), w(nxd) |
|---|
| 664 | real*8 z(nxd),z2(nxd) |
|---|
| 665 | real*8 x(nxd),x2(nxd) |
|---|
| 666 | |
|---|
| 667 | integer terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
|---|
| 668 | common /setup/ terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
|---|
| 669 | |
|---|
| 670 | integer nlow,nhigh,nx,nxx,dn,version,isteps |
|---|
| 671 | common /ivariables/ nlow,nhigh,nx,nxx,version,isteps |
|---|
| 672 | |
|---|
| 673 | real*8 toll,cfl,theta |
|---|
| 674 | real*8 g,hf,dx,dt,dtmax |
|---|
| 675 | real*8 Tout,tf,tc,uhf |
|---|
| 676 | real*8 K,limith,length |
|---|
| 677 | real*8 manning,hl,hr |
|---|
| 678 | common /rvariables/ toll,cfl,theta, |
|---|
| 679 | . g,hf,dx,dt,dtmax, |
|---|
| 680 | . Tout,tf,tc,uhf, |
|---|
| 681 | . K,limith,length, |
|---|
| 682 | . manning,hl,hr |
|---|
| 683 | |
|---|
| 684 | real*8 du,dh,uf,h0,u0,uh0 |
|---|
| 685 | integer ii,i |
|---|
| 686 | |
|---|
| 687 | c-------------------------------------------------- |
|---|
| 688 | |
|---|
| 689 | do i = 1, md |
|---|
| 690 | c================== |
|---|
| 691 | c Left Boundary |
|---|
| 692 | c================== |
|---|
| 693 | |
|---|
| 694 | c --- Zero |
|---|
| 695 | h(i) = 0.d0 |
|---|
| 696 | uh(i) = 0.d0 |
|---|
| 697 | end do |
|---|
| 698 | |
|---|
| 699 | do i = 1, md |
|---|
| 700 | c================== |
|---|
| 701 | c Right Boundary |
|---|
| 702 | c================== |
|---|
| 703 | |
|---|
| 704 | c --- Zero |
|---|
| 705 | h(nx+md+i) = 0.d0 |
|---|
| 706 | uh(nx+md+i) = 0.d0 |
|---|
| 707 | c h(nx+md+1) = h(nx-1) |
|---|
| 708 | c uh(nx+md+1) = uh(nx-1) |
|---|
| 709 | end do |
|---|
| 710 | |
|---|
| 711 | return |
|---|
| 712 | end |
|---|
| 713 | c=========================================================== |
|---|
| 714 | c Numerical Central Flux |
|---|
| 715 | c=========================================================== |
|---|
| 716 | subroutine numerical_flux_central(h,uh,z2,z,uh_l,uh_r,h_l,h_r, |
|---|
| 717 | . h_2,f_h,f_uh, em_x) |
|---|
| 718 | |
|---|
| 719 | implicit none |
|---|
| 720 | integer md,nxmax,nxd, mn |
|---|
| 721 | parameter (md=3, nxmax=5000, nxd=nxmax+2*md, mn=2) |
|---|
| 722 | real*8 h(nxd), uh(nxd), w(nxd) |
|---|
| 723 | real*8 z(nxd),z2(nxd) |
|---|
| 724 | real*8 x(nxd),x2(nxd) |
|---|
| 725 | |
|---|
| 726 | c integer terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
|---|
| 727 | c common /setup/ terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
|---|
| 728 | |
|---|
| 729 | integer nlow,nhigh,nx,nxx,dn,version,isteps |
|---|
| 730 | common /ivariables/ nlow,nhigh,nx,nxx,version,isteps |
|---|
| 731 | |
|---|
| 732 | real*8 toll,cfl,theta |
|---|
| 733 | real*8 g,hf,dx,dt,dtmax |
|---|
| 734 | real*8 Tout,tf,tc,uhf |
|---|
| 735 | real*8 K,limith,length |
|---|
| 736 | real*8 manning,hl,hr |
|---|
| 737 | common /rvariables/ toll,cfl,theta, |
|---|
| 738 | . g,hf,dx,dt,dtmax, |
|---|
| 739 | . Tout,tf,tc,uhf, |
|---|
| 740 | . K,limith,length, |
|---|
| 741 | . manning,hl,hr |
|---|
| 742 | |
|---|
| 743 | real*8 f_h(nxd), f_uh(nxd) |
|---|
| 744 | real*8 h_2(nxd), uh_2(nxd) |
|---|
| 745 | real*8 h_l(nxd), h_r(nxd), uh_l(nxd), uh_r(nxd) |
|---|
| 746 | |
|---|
| 747 | |
|---|
| 748 | real*8 fh_l, fuh_l, fh_r, fuh_r |
|---|
| 749 | real*8 l1_l, l2_l, l1_r, l2_r |
|---|
| 750 | real*8 a_max, a_min, aa, axa |
|---|
| 751 | |
|---|
| 752 | integer istop,iout,nt,ii,oi,i2,m,i |
|---|
| 753 | real*8 a,b,t,Tleft,em_x,dtcdx,dtcdx2,dtcdx3 |
|---|
| 754 | c real*8 den, xmt,pre, Tnext, em_old, hh |
|---|
| 755 | c real*8 aterm1 ,term1, aterm2 ,term2, aterm3 ,term3 |
|---|
| 756 | |
|---|
| 757 | c----------------------------------- |
|---|
| 758 | |
|---|
| 759 | em_x = 1.0d-15 |
|---|
| 760 | |
|---|
| 761 | do i = md,nxx-md+1 |
|---|
| 762 | |
|---|
| 763 | c |
|---|
| 764 | c ---- Calculate flux |
|---|
| 765 | c |
|---|
| 766 | |
|---|
| 767 | call flux_huh(fh_l,fuh_l,h_r(i),uh_r(i), |
|---|
| 768 | . em_x,l1_l,l2_l,g,toll) |
|---|
| 769 | call flux_huh(fh_r,fuh_r,h_l(i+1),uh_l(i+1), |
|---|
| 770 | . em_x,l1_r,l2_r,g,toll) |
|---|
| 771 | c |
|---|
| 772 | c --- Calculate max wave speed |
|---|
| 773 | c |
|---|
| 774 | a_max = dmax1(l2_l,l2_r,0.0d0) |
|---|
| 775 | a_min = dmin1(l1_l,l1_r,0.0d0) |
|---|
| 776 | c |
|---|
| 777 | c --- Compute the numerical flux |
|---|
| 778 | c |
|---|
| 779 | aa = a_max - a_min |
|---|
| 780 | axa = a_max*a_min |
|---|
| 781 | if ( aa .gt. dx*dt/1000.0d0) then |
|---|
| 782 | h_2(i) =(a_max*h_l(i+1) - a_min*h_r(i) - |
|---|
| 783 | . fh_r + fh_l )/aa |
|---|
| 784 | f_h(i) =(a_max*fh_l - a_min*fh_r + |
|---|
| 785 | . axa*(h_l(i+1)-h_r(i)))/aa |
|---|
| 786 | f_uh(i) =(a_max*fuh_l - a_min*fuh_r + |
|---|
| 787 | . axa*(uh_l(i+1)-uh_r(i)))/aa |
|---|
| 788 | else |
|---|
| 789 | h_2(i) = 0.0d0 |
|---|
| 790 | f_h(i) = 0.0d0 |
|---|
| 791 | f_uh(i) = 0.0d0 |
|---|
| 792 | endif |
|---|
| 793 | |
|---|
| 794 | enddo |
|---|
| 795 | |
|---|
| 796 | return |
|---|
| 797 | end |
|---|
| 798 | c=========================================================== |
|---|
| 799 | c Open Files |
|---|
| 800 | c=========================================================== |
|---|
| 801 | subroutine util_open_files |
|---|
| 802 | |
|---|
| 803 | open(11,file='data.w') |
|---|
| 804 | open(12,file='data.t') |
|---|
| 805 | open(13,file='data.h') |
|---|
| 806 | open(14,file='data.uh') |
|---|
| 807 | open(15,file='data.n') |
|---|
| 808 | open(16,file='data.x') |
|---|
| 809 | |
|---|
| 810 | |
|---|
| 811 | open(25,file='data.xx') |
|---|
| 812 | |
|---|
| 813 | return |
|---|
| 814 | end |
|---|
| 815 | c=========================================================== |
|---|
| 816 | c Close Files |
|---|
| 817 | c=========================================================== |
|---|
| 818 | subroutine util_close_files |
|---|
| 819 | |
|---|
| 820 | close(11) |
|---|
| 821 | close(12) |
|---|
| 822 | close(13) |
|---|
| 823 | close(14) |
|---|
| 824 | close(15) |
|---|
| 825 | close(16) |
|---|
| 826 | |
|---|
| 827 | close(25) |
|---|
| 828 | |
|---|
| 829 | return |
|---|
| 830 | end |
|---|
