| 1 | program sfbasic |
|---|
| 2 | c============================================================ |
|---|
| 3 | c Combine evolution of w = h+z and h for shallow flows |
|---|
| 4 | c============================================================ |
|---|
| 5 | |
|---|
| 6 | implicit none |
|---|
| 7 | |
|---|
| 8 | integer md,nxmax,nxd, mn |
|---|
| 9 | |
|---|
| 10 | parameter (md=3, nxmax=5000, nxd=nxmax+2*md, mn=2) |
|---|
| 11 | real*8 h(nxd), uh(nxd), w(nxd) |
|---|
| 12 | real*8 z(nxd),z2(nxd) |
|---|
| 13 | real*8 x(nxd),x2(nxd) |
|---|
| 14 | |
|---|
| 15 | integer terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
|---|
| 16 | common /setup/ terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
|---|
| 17 | |
|---|
| 18 | integer nlow,nhigh,nx,nxx,dn,version,isteps |
|---|
| 19 | common /ivariables/ nlow,nhigh,nx,nxx,version,isteps |
|---|
| 20 | |
|---|
| 21 | real*8 toll,cfl,theta |
|---|
| 22 | real*8 g,hf,dx,dt,dtmax |
|---|
| 23 | real*8 Tout,tf,tc,uhf |
|---|
| 24 | real*8 K,limith,length |
|---|
| 25 | real*8 manning,hl,hr,zb |
|---|
| 26 | common /rvariables/ toll,cfl,theta, |
|---|
| 27 | . g,hf,dx,dt,dtmax, |
|---|
| 28 | . Tout,tf,tc,uhf, |
|---|
| 29 | . K,limith,length, |
|---|
| 30 | . manning,hl,hr |
|---|
| 31 | |
|---|
| 32 | integer io, i |
|---|
| 33 | |
|---|
| 34 | call util_open_files |
|---|
| 35 | |
|---|
| 36 | open(1,file='MacDonald.bed') |
|---|
| 37 | c |
|---|
| 38 | c Parameters |
|---|
| 39 | c |
|---|
| 40 | nx = 101 |
|---|
| 41 | dtmax = 0.5d0 |
|---|
| 42 | Tout = 1.0d0 |
|---|
| 43 | tf = 1500.0d0 |
|---|
| 44 | length = 1000.0d0 |
|---|
| 45 | |
|---|
| 46 | nlow = md+2 |
|---|
| 47 | nhigh = md+nx |
|---|
| 48 | nxx = nx+2*md |
|---|
| 49 | |
|---|
| 50 | limith = 1 |
|---|
| 51 | |
|---|
| 52 | dx = 10000.d0/dble(nx-1) |
|---|
| 53 | K = 0.0d0 |
|---|
| 54 | |
|---|
| 55 | if (nx.gt.nxmax) write(*,*)'nx too large' |
|---|
| 56 | toll = 1.0d-10 |
|---|
| 57 | cfl = 0.2d0 |
|---|
| 58 | theta = 1.2d0 |
|---|
| 59 | version = 10 |
|---|
| 60 | g = 9.81d0 |
|---|
| 61 | hl = 5.d0 |
|---|
| 62 | hr = 0.d0 |
|---|
| 63 | tc = 0.d0 |
|---|
| 64 | |
|---|
| 65 | c |
|---|
| 66 | c ---- Setup Terrain, Boundary Values and Initial Values |
|---|
| 67 | c |
|---|
| 68 | |
|---|
| 69 | c ---- Non-uniform terrain from MacDonald |
|---|
| 70 | do i = 1,nxx |
|---|
| 71 | read(1,*)x2(i),z2(i) |
|---|
| 72 | z2(i) = z2(i)*5.d0 |
|---|
| 73 | x(i) = x2(i) - dx/2.d0 |
|---|
| 74 | end do |
|---|
| 75 | do i = 2,nxx |
|---|
| 76 | z(i) = (z2(i-1)+z2(i))/2.d0 |
|---|
| 77 | end do |
|---|
| 78 | z(1) = (3.d0*z2(1) - z2(2))/2.d0 |
|---|
| 79 | z(nxx) = (3.d0*z2(nxx-1) - z2(nxx-2))/2.d0 |
|---|
| 80 | |
|---|
| 81 | call boundary_apply(x,h,uh,z) |
|---|
| 82 | |
|---|
| 83 | c ---- Rectangular pulse initial condition |
|---|
| 84 | do i = md+1, nx+md |
|---|
| 85 | if (x(i).lt.100.d0.or.x(i).gt.200.d0) then |
|---|
| 86 | h(i) = hr |
|---|
| 87 | else |
|---|
| 88 | h(i) = hl |
|---|
| 89 | endif |
|---|
| 90 | uh(i) = 0.0d0 |
|---|
| 91 | end do |
|---|
| 92 | c |
|---|
| 93 | c ---- Setup for Time looping |
|---|
| 94 | c |
|---|
| 95 | isteps = 0 |
|---|
| 96 | tc = 0.0d0 |
|---|
| 97 | call util_dump_solution(h,uh,z) |
|---|
| 98 | c |
|---|
| 99 | c ---- Evolve |
|---|
| 100 | c |
|---|
| 101 | call evolver_euler(x,h,uh,z,z2) |
|---|
| 102 | c |
|---|
| 103 | c ---- Close down |
|---|
| 104 | c |
|---|
| 105 | write(15,*)isteps,nxx,version |
|---|
| 106 | do i=1,nxx |
|---|
| 107 | write(16,*) x(i) |
|---|
| 108 | enddo |
|---|
| 109 | |
|---|
| 110 | do i=5,nxx-3 |
|---|
| 111 | write(25,*) x(i) |
|---|
| 112 | enddo |
|---|
| 113 | |
|---|
| 114 | call util_close_files |
|---|
| 115 | |
|---|
| 116 | stop |
|---|
| 117 | end |
|---|
| 118 | c=========================================================== |
|---|
| 119 | c Shallow Water Flux |
|---|
| 120 | c=========================================================== |
|---|
| 121 | subroutine flux_huh(f1,f2,h0,uh0,em_x,l1,l2,g,toll) |
|---|
| 122 | implicit none |
|---|
| 123 | |
|---|
| 124 | real*8 f1,f2,h0,uh0,z,l1,l2 |
|---|
| 125 | real*8 em_x,g,toll |
|---|
| 126 | |
|---|
| 127 | real*8 u,cvel,h,uh,w |
|---|
| 128 | integer i |
|---|
| 129 | |
|---|
| 130 | c----------------------------------- |
|---|
| 131 | |
|---|
| 132 | if(em_x.lt.1.0d-15) then |
|---|
| 133 | em_x = 1.d-15 |
|---|
| 134 | endif |
|---|
| 135 | |
|---|
| 136 | uh = uh0 |
|---|
| 137 | h = h0 |
|---|
| 138 | |
|---|
| 139 | if(h.le.toll)then |
|---|
| 140 | u = 0.d0 |
|---|
| 141 | h = 0.0d0 |
|---|
| 142 | uh = 0.0d0 |
|---|
| 143 | else |
|---|
| 144 | u = uh/h |
|---|
| 145 | endif |
|---|
| 146 | |
|---|
| 147 | cvel = dsqrt( g*h ) |
|---|
| 148 | l1 = u - cvel |
|---|
| 149 | l2 = u + cvel |
|---|
| 150 | em_x = dmax1( em_x, dabs(u) + cvel ) |
|---|
| 151 | f1 = uh |
|---|
| 152 | f2 = uh*u + 0.5d0*g*h**2 |
|---|
| 153 | |
|---|
| 154 | return |
|---|
| 155 | end |
|---|
| 156 | c=========================================================== |
|---|
| 157 | c Shallow Water Flux |
|---|
| 158 | c=========================================================== |
|---|
| 159 | subroutine flux_huh_old(f1,f2,h0,uh0,z,em_x,l1,l2,g,toll) |
|---|
| 160 | implicit none |
|---|
| 161 | |
|---|
| 162 | real*8 f1,f2,h0,uh0,z,l1,l2 |
|---|
| 163 | real*8 em_x,g,toll |
|---|
| 164 | |
|---|
| 165 | real*8 u,cvel,h,uh,w |
|---|
| 166 | integer i |
|---|
| 167 | |
|---|
| 168 | c----------------------------------- |
|---|
| 169 | |
|---|
| 170 | if(em_x.lt.1.0d-15) then |
|---|
| 171 | em_x = 1.d-15 |
|---|
| 172 | endif |
|---|
| 173 | |
|---|
| 174 | w = h0+z |
|---|
| 175 | uh = uh0 |
|---|
| 176 | h = h0 |
|---|
| 177 | |
|---|
| 178 | if(h.le.toll)then |
|---|
| 179 | u = 0.d0 |
|---|
| 180 | h = 0.0d0 |
|---|
| 181 | uh = 0.0d0 |
|---|
| 182 | else |
|---|
| 183 | u = uh / h |
|---|
| 184 | endif |
|---|
| 185 | if (abs(u).gt.1.0d1) then |
|---|
| 186 | u = dsign(1.0d0,u)*1.0d3 |
|---|
| 187 | uh = u*h |
|---|
| 188 | end if |
|---|
| 189 | cvel = dsqrt( g*h ) |
|---|
| 190 | l1 = u - cvel |
|---|
| 191 | l2 = u + cvel |
|---|
| 192 | em_x = dmax1( em_x, dabs(u) + cvel ) |
|---|
| 193 | f1 = uh |
|---|
| 194 | f2 = uh*u + 0.5d0*g*h**2 |
|---|
| 195 | |
|---|
| 196 | return |
|---|
| 197 | end |
|---|
| 198 | c=========================================================== |
|---|
| 199 | c Shallow Water Flux using h+z and uh variables |
|---|
| 200 | c=========================================================== |
|---|
| 201 | subroutine flux_wuh(f1,f2,w0,uh0,z,em_x,l1,l2,g,toll) |
|---|
| 202 | implicit none |
|---|
| 203 | |
|---|
| 204 | real*8 f1,f2,w0,uh0,z |
|---|
| 205 | real*8 g,toll |
|---|
| 206 | |
|---|
| 207 | real*8 h,u,cvel,uh,w,l1,l2,em_x |
|---|
| 208 | integer i |
|---|
| 209 | |
|---|
| 210 | c----------------------------------- |
|---|
| 211 | |
|---|
| 212 | if(em_x.lt.1.0d-15) then |
|---|
| 213 | em_x = 1.d-15 |
|---|
| 214 | endif |
|---|
| 215 | |
|---|
| 216 | w = w0 |
|---|
| 217 | uh = uh0 |
|---|
| 218 | |
|---|
| 219 | h = w - z |
|---|
| 220 | if(h.le.toll)then |
|---|
| 221 | u = 0.d0 |
|---|
| 222 | h = 0.0d0 |
|---|
| 223 | uh = 0.0d0 |
|---|
| 224 | else |
|---|
| 225 | u = uh / h |
|---|
| 226 | endif |
|---|
| 227 | if (abs(u).gt.1.0d3) then |
|---|
| 228 | u = dsign(1.0d0,u)*1.0d3 |
|---|
| 229 | uh = u*h |
|---|
| 230 | end if |
|---|
| 231 | cvel = dsqrt( g*h ) |
|---|
| 232 | l1 = u - cvel |
|---|
| 233 | l2 = u + cvel |
|---|
| 234 | em_x = dmax1( em_x, dabs(u) + cvel ) |
|---|
| 235 | f1 = uh |
|---|
| 236 | f2 = uh*u + 0.5d0*g*h**2 |
|---|
| 237 | |
|---|
| 238 | return |
|---|
| 239 | end |
|---|
| 240 | c=============================================================== |
|---|
| 241 | c array limiter |
|---|
| 242 | c=============================================================== |
|---|
| 243 | subroutine array_limit_h(h,uh,z2,z,uh_l,uh_r,h_l,h_r,h_2) |
|---|
| 244 | |
|---|
| 245 | implicit none |
|---|
| 246 | integer md,nxmax,nxd, mn |
|---|
| 247 | parameter (md=3, nxmax=5000, nxd=nxmax+2*md, mn=2) |
|---|
| 248 | real*8 h(nxd), uh(nxd), w(nxd) |
|---|
| 249 | real*8 z(nxd),z2(nxd) |
|---|
| 250 | real*8 x(nxd),x2(nxd) |
|---|
| 251 | |
|---|
| 252 | integer terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
|---|
| 253 | common /setup/ terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
|---|
| 254 | |
|---|
| 255 | integer nlow,nhigh,nx,nxx,dn,version,isteps |
|---|
| 256 | common /ivariables/ nlow,nhigh,nx,nxx,version,isteps |
|---|
| 257 | |
|---|
| 258 | real*8 toll,cfl,theta |
|---|
| 259 | real*8 g,hf,dx,dt,dtmax |
|---|
| 260 | real*8 Tout,tf,tc,uhf |
|---|
| 261 | real*8 K,limith,length |
|---|
| 262 | real*8 manning,hl,hr |
|---|
| 263 | common /rvariables/ toll,cfl,theta, |
|---|
| 264 | . g,hf,dx,dt,dtmax, |
|---|
| 265 | . Tout,tf,tc,uhf, |
|---|
| 266 | . K,limith,length, |
|---|
| 267 | . manning,hl,hr |
|---|
| 268 | |
|---|
| 269 | real*8 h_2(nxd) |
|---|
| 270 | real*8 h_l(nxd),h_r(nxd) |
|---|
| 271 | real*8 h1_l(nxd), h1_r(nxd) |
|---|
| 272 | real*8 uh_l(nxd), uh_r(nxd) |
|---|
| 273 | |
|---|
| 274 | integer sslope(nxd) |
|---|
| 275 | real*8 xmin,xmic,xminmod,a,b,c,t |
|---|
| 276 | |
|---|
| 277 | xmin(a,b) = 0.5d0*(dsign(1.d0,a)+dsign(1.d0,b))* |
|---|
| 278 | . dmin1(dabs(a),dabs(b)) |
|---|
| 279 | xmic(t,a,b) = xmin(t*xmin(a,b), 0.5d0*(a+b) ) |
|---|
| 280 | xminmod(a,b,c) = xmin(a,xmin(b,c)) |
|---|
| 281 | |
|---|
| 282 | |
|---|
| 283 | integer i |
|---|
| 284 | real*8 dh, hmax, hmin , tt, cc |
|---|
| 285 | real*8 w0,w1,w2,d0h,d0w,d1h,d1w,d2h,d2w,ddh,ddw |
|---|
| 286 | real*8 h0,h1,h2,hz |
|---|
| 287 | real*8 ss0,ss1,ss |
|---|
| 288 | real*8 dz0,dz1,dz2 |
|---|
| 289 | real*8 hx1,hx2,h_x |
|---|
| 290 | real*8 froud,d1,d2 |
|---|
| 291 | real*8 gh3,uh2,duh, w_x,dz |
|---|
| 292 | |
|---|
| 293 | c------------------------------------ |
|---|
| 294 | g = 9.81d0 |
|---|
| 295 | cc = 0.1d0 |
|---|
| 296 | ss0 = 0.01d0 |
|---|
| 297 | ss1 = 0.01d0 |
|---|
| 298 | |
|---|
| 299 | do i=md,nx+md+2 |
|---|
| 300 | |
|---|
| 301 | h_2(i) = h(i) |
|---|
| 302 | h0 = h(i-1) |
|---|
| 303 | h1 = h(i) |
|---|
| 304 | h2 = h(i+1) |
|---|
| 305 | |
|---|
| 306 | dz0 = abs(z2(i-1)-z2(i-2)) |
|---|
| 307 | dz1 = abs(z2(i) -z2(i-1)) |
|---|
| 308 | dz2 = abs(z2(i+1)-z2(i) ) |
|---|
| 309 | |
|---|
| 310 | w0 = h0 + z(i-1) |
|---|
| 311 | w1 = h1 + z(i) |
|---|
| 312 | w2 = h2 + z(i+1) |
|---|
| 313 | |
|---|
| 314 | d1h = h1 - h0 |
|---|
| 315 | d2h = h2 - h1 |
|---|
| 316 | d1w = w1 - w0 |
|---|
| 317 | d2w = w2 - w1 |
|---|
| 318 | dz = (z2(i) - z2(i-1)) |
|---|
| 319 | |
|---|
| 320 | c ------- W = H+Z |
|---|
| 321 | c h_x = xmin( d1w, d2w) - dz |
|---|
| 322 | h_x = xmic(theta, d1h, d2h) |
|---|
| 323 | |
|---|
| 324 | c ------- Return the left and right values of h in an interval |
|---|
| 325 | h_l(i) = h(i) - 0.5d0*h_x |
|---|
| 326 | h_r(i) = h(i) + 0.5d0*h_x |
|---|
| 327 | |
|---|
| 328 | c ------- Test for h_l or h_r negative |
|---|
| 329 | c$$$ hmin = dmin1(h0,h1,h2) |
|---|
| 330 | c$$$ if ( h_l(i) .le. hmin ) then |
|---|
| 331 | c$$$ h_l(i) = hmin |
|---|
| 332 | c$$$ h_r(i) = h(i) + (h(i) - h_l(i)) |
|---|
| 333 | c$$$ elseif ( h_r(i) .le. hmin ) then |
|---|
| 334 | c$$$ h_r(i) = hmin |
|---|
| 335 | c$$$ h_l(i) = h(i) + (h(i) - h_r(i)) |
|---|
| 336 | c$$$ endif |
|---|
| 337 | enddo |
|---|
| 338 | c |
|---|
| 339 | c ---- Enforce a minimum height |
|---|
| 340 | c |
|---|
| 341 | c$$$ do i=md,nx+md+2 |
|---|
| 342 | c$$$ hmax = dmax1(h_l(i),h_r(i)) |
|---|
| 343 | c$$$ if (hmax .lt. 1.0d-3 ) then |
|---|
| 344 | c$$$c h_r(i) = 0.0d0 |
|---|
| 345 | c$$$ uh_r(i) = 0.0d0 |
|---|
| 346 | c$$$c h_l(i) = 0.0d0 |
|---|
| 347 | c$$$ uh_l(i) = 0.0d0 |
|---|
| 348 | c$$$c h(i) = 0.0d0 |
|---|
| 349 | c$$$ uh(i) = 0.0d0 |
|---|
| 350 | c$$$ endif |
|---|
| 351 | c$$$ enddo |
|---|
| 352 | c |
|---|
| 353 | c ---- Try for a flat subinterval |
|---|
| 354 | cc |
|---|
| 355 | c do i=md,nx+md+2 |
|---|
| 356 | c hmax = dmax1(h_l(i),h_r(i)) |
|---|
| 357 | c dz = (z2(i) - z2(i-1)) |
|---|
| 358 | c |
|---|
| 359 | c if (h_l(i) .lt. 0.01d0*h_r(i) ) then |
|---|
| 360 | c h_r(i) = sqrt(abs(2.0d0*dz*h(i))) |
|---|
| 361 | c endif |
|---|
| 362 | c |
|---|
| 363 | c if (h_r(i) .lt. 0.01d0*h_l(i) ) then |
|---|
| 364 | c h_l(i) = sqrt(abs(2.0d0*dz*h(i))) |
|---|
| 365 | c endif |
|---|
| 366 | c enddo |
|---|
| 367 | |
|---|
| 368 | return |
|---|
| 369 | end |
|---|
| 370 | c=============================================================== |
|---|
| 371 | c array limiter |
|---|
| 372 | c=============================================================== |
|---|
| 373 | subroutine array_limit(u,u_l,u_r) |
|---|
| 374 | |
|---|
| 375 | implicit none |
|---|
| 376 | integer md,nxmax,nxd, mn |
|---|
| 377 | parameter (md=3, nxmax=5000, nxd=nxmax+2*md, mn=2) |
|---|
| 378 | real*8 h(nxd), uh(nxd), w(nxd) |
|---|
| 379 | real*8 z(nxd),z2(nxd) |
|---|
| 380 | real*8 x(nxd),x2(nxd) |
|---|
| 381 | |
|---|
| 382 | integer terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
|---|
| 383 | common /setup/ terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
|---|
| 384 | |
|---|
| 385 | integer nlow,nhigh,nx,nxx,dn,version,isteps |
|---|
| 386 | common /ivariables/ nlow,nhigh,nx,nxx,version,isteps |
|---|
| 387 | |
|---|
| 388 | real*8 toll,cfl,theta |
|---|
| 389 | real*8 g,hf,dx,dt,dtmax |
|---|
| 390 | real*8 Tout,tf,tc,uhf |
|---|
| 391 | real*8 K,limith,length |
|---|
| 392 | real*8 manning,hl,hr |
|---|
| 393 | common /rvariables/ toll,cfl,theta, |
|---|
| 394 | . g,hf,dx,dt,dtmax, |
|---|
| 395 | . Tout,tf,tc,uhf, |
|---|
| 396 | . K,limith,length, |
|---|
| 397 | . manning,hl,hr |
|---|
| 398 | |
|---|
| 399 | real*8 u(nxd), u_l(nxd),u_r(nxd) |
|---|
| 400 | real*8 u_x,d1,d2,d0,ux1 |
|---|
| 401 | real*8 u1_l(nxd),u1_r(nxd) |
|---|
| 402 | integer i |
|---|
| 403 | |
|---|
| 404 | real*8 a,b,t,xmin,xmic |
|---|
| 405 | |
|---|
| 406 | xmin(a,b) = 0.5d0*(dsign(1.d0,a)+dsign(1.d0,b))* |
|---|
| 407 | . dmin1(dabs(a),dabs(b)) |
|---|
| 408 | xmic(t,a,b) = xmin(t*xmin(a,b), 0.5d0*(a+b) ) |
|---|
| 409 | |
|---|
| 410 | c------------------------------------ |
|---|
| 411 | |
|---|
| 412 | do i=md,nx+md+2 |
|---|
| 413 | d1 = u(i) - u(i-1) |
|---|
| 414 | d2 = u(i+1) - u(i) |
|---|
| 415 | u_x = xmic( theta, d1, d2 ) |
|---|
| 416 | c u_x = xmin( d1, d2 ) |
|---|
| 417 | u_l(i) = u(i) - 0.5d0*u_x |
|---|
| 418 | u_r(i) = u(i) + 0.5d0*u_x |
|---|
| 419 | enddo |
|---|
| 420 | |
|---|
| 421 | return |
|---|
| 422 | end |
|---|
| 423 | c=========================================================== |
|---|
| 424 | c Output Routine |
|---|
| 425 | c=========================================================== |
|---|
| 426 | subroutine util_dump_solution(h,uh,z) |
|---|
| 427 | |
|---|
| 428 | implicit none |
|---|
| 429 | integer md,nxmax,nxd, mn |
|---|
| 430 | parameter (md=3, nxmax=5000, nxd=nxmax+2*md, mn=2) |
|---|
| 431 | real*8 h(nxd), uh(nxd), w(nxd) |
|---|
| 432 | real*8 z(nxd),z2(nxd) |
|---|
| 433 | real*8 x(nxd),x2(nxd) |
|---|
| 434 | |
|---|
| 435 | integer terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
|---|
| 436 | common /setup/ terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
|---|
| 437 | |
|---|
| 438 | integer nlow,nhigh,nx,nxx,dn,version,isteps |
|---|
| 439 | common /ivariables/ nlow,nhigh,nx,nxx,version,isteps |
|---|
| 440 | |
|---|
| 441 | real*8 toll,cfl,theta |
|---|
| 442 | real*8 g,hf,dx,dt,dtmax |
|---|
| 443 | real*8 Tout,tf,tc,uhf |
|---|
| 444 | real*8 K,limith,length |
|---|
| 445 | real*8 manning,hl,hr |
|---|
| 446 | common /rvariables/ toll,cfl,theta, |
|---|
| 447 | . g,hf,dx,dt,dtmax, |
|---|
| 448 | . Tout,tf,tc,uhf, |
|---|
| 449 | . K,limith,length, |
|---|
| 450 | . manning,hl,hr |
|---|
| 451 | |
|---|
| 452 | integer ii,i |
|---|
| 453 | |
|---|
| 454 | write(12,*)tc |
|---|
| 455 | |
|---|
| 456 | isteps = isteps + 1 |
|---|
| 457 | write(*,*)isteps, tc |
|---|
| 458 | |
|---|
| 459 | do i = 1, nx+2*md |
|---|
| 460 | c------ Dump h |
|---|
| 461 | write(13,200)sngl(h(i)) |
|---|
| 462 | c------ Dump uh |
|---|
| 463 | write(14,200)sngl(uh(i)) |
|---|
| 464 | c------ Dump w |
|---|
| 465 | write(11,200)sngl(h(i)+z(i)) |
|---|
| 466 | 200 format(e20.8) |
|---|
| 467 | end do |
|---|
| 468 | |
|---|
| 469 | return |
|---|
| 470 | end |
|---|
| 471 | c=============================================================== |
|---|
| 472 | c The evolver using euler's method |
|---|
| 473 | c=============================================================== |
|---|
| 474 | subroutine evolver_euler(x,h,uh,z,z2) |
|---|
| 475 | |
|---|
| 476 | implicit none |
|---|
| 477 | integer md,nxmax,nxd, mn |
|---|
| 478 | parameter (md=3, nxmax=5000, nxd=nxmax+2*md, mn=2) |
|---|
| 479 | real*8 h(nxd), uh(nxd), w(nxd) |
|---|
| 480 | real*8 z(nxd),z2(nxd) |
|---|
| 481 | real*8 x(nxd),x2(nxd) |
|---|
| 482 | |
|---|
| 483 | integer terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
|---|
| 484 | c common /setup/ terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
|---|
| 485 | |
|---|
| 486 | integer nlow,nhigh,nx,nxx,dn,version,isteps |
|---|
| 487 | common /ivariables/ nlow,nhigh,nx,nxx,version,isteps |
|---|
| 488 | |
|---|
| 489 | real*8 toll,cfl,theta |
|---|
| 490 | real*8 g,hf,dx,dt,dtmax |
|---|
| 491 | real*8 Tout,tf,tc,uhf |
|---|
| 492 | real*8 K,limith,length |
|---|
| 493 | real*8 manning,hl,hr |
|---|
| 494 | common /rvariables/ toll,cfl,theta, |
|---|
| 495 | . g,hf,dx,dt,dtmax, |
|---|
| 496 | . Tout,tf,tc,uhf, |
|---|
| 497 | . K,limith,length, |
|---|
| 498 | . manning,hl,hr |
|---|
| 499 | |
|---|
| 500 | real*8 h_new(nxd),uh_new(nxd) |
|---|
| 501 | real*8 h_h(nxd),uh_h(nxd) |
|---|
| 502 | real*8 h_h_x(nxd),uh_h_x(nxd) |
|---|
| 503 | real*8 h_x(nxd), uh_x(nxd) |
|---|
| 504 | real*8 f_h(nxd), f_uh(nxd) |
|---|
| 505 | real*8 f_h_l(nxd), f_uh_l(nxd) |
|---|
| 506 | real*8 f_h_r(nxd), f_uh_r(nxd) |
|---|
| 507 | real*8 z_l(nxd),z_r(nxd) |
|---|
| 508 | real*8 h_2(nxd), uh_2(nxd) |
|---|
| 509 | |
|---|
| 510 | real*8 h_l(nxd), h_r(nxd), uh_l(nxd), uh_r(nxd) |
|---|
| 511 | real*8 z2l, z2r, zl, zr |
|---|
| 512 | |
|---|
| 513 | integer io, i, jj, ipos,ip |
|---|
| 514 | real*8 factor, Ki |
|---|
| 515 | |
|---|
| 516 | integer istop,iout,nt,ii,oi,i2,m |
|---|
| 517 | real*8 a,b,t,Tleft,em_x,dtcdx,dtcdx2,dtcdx3 |
|---|
| 518 | real*8 den, xmt,pre, Tnext, em_old, hh |
|---|
| 519 | real*8 aterm1 ,term1, aterm2 ,term2, aterm3 ,term3 |
|---|
| 520 | |
|---|
| 521 | integer kk |
|---|
| 522 | real*8 umax, umax2, vmin, q1,q2,q3,h1,h2 |
|---|
| 523 | real*8 Kcal,k1,k2,za,zb,pi |
|---|
| 524 | |
|---|
| 525 | real*8 fh_l, fuh_l, fh_r, fuh_r |
|---|
| 526 | real*8 l1_l, l2_l, l1_r, l2_r |
|---|
| 527 | real*8 a_max, a_min, aa, axa |
|---|
| 528 | |
|---|
| 529 | c---------------------------------------------------------- |
|---|
| 530 | c |
|---|
| 531 | pi = 2.d0*dtan(1.d0) |
|---|
| 532 | factor = 1.0d0 |
|---|
| 533 | em_old = 1.0d0 |
|---|
| 534 | tc = 0.d0 |
|---|
| 535 | istop = 0 |
|---|
| 536 | iout = 0 |
|---|
| 537 | nt =0 |
|---|
| 538 | Tleft = dmin1(Tout,tf) |
|---|
| 539 | Tnext = dmin1(Tout,tf) |
|---|
| 540 | dt = dmin1(dtmax,Tleft) |
|---|
| 541 | |
|---|
| 542 | do i=1,nxx |
|---|
| 543 | f_h(i) = 0.0d0 |
|---|
| 544 | f_uh(i) = 0.0d0 |
|---|
| 545 | h_l(i) = h(i) |
|---|
| 546 | h_r(i) = h(i) |
|---|
| 547 | uh_l(i) = uh(i) |
|---|
| 548 | uh_r(i) = uh(i) |
|---|
| 549 | enddo |
|---|
| 550 | |
|---|
| 551 | call boundary_apply(x,h,uh,z) |
|---|
| 552 | call array_limit (uh,uh_l,uh_r) |
|---|
| 553 | call array_limit_h(h,uh,z2,z,uh_l,uh_r,h_l,h_r,h_2) |
|---|
| 554 | |
|---|
| 555 | do i=1,nxx |
|---|
| 556 | if ( h(i) .lt. 0.0d0 ) then |
|---|
| 557 | write(*,*)'i=',i,' h(i) = ',h(i) |
|---|
| 558 | endif |
|---|
| 559 | enddo |
|---|
| 560 | |
|---|
| 561 | c------------------------------------------------------ |
|---|
| 562 | c |
|---|
| 563 | do while (.true.) |
|---|
| 564 | c write(*,*)nt |
|---|
| 565 | nt = nt+1 |
|---|
| 566 | ii = 1 |
|---|
| 567 | |
|---|
| 568 | call boundary_apply(x,h,uh,z) |
|---|
| 569 | |
|---|
| 570 | call array_limit (uh,uh_l,uh_r) |
|---|
| 571 | call array_limit_h(h,uh,z2,z,uh_l,uh_r,h_l,h_r,h_2) |
|---|
| 572 | |
|---|
| 573 | do i=1,nxx |
|---|
| 574 | if ( h(i) .lt. 0.0d0 ) then |
|---|
| 575 | write(*,*)'i=',i,' h(i) = ',h(i),' nt = ',nt |
|---|
| 576 | endif |
|---|
| 577 | enddo |
|---|
| 578 | |
|---|
| 579 | c------------------------- |
|---|
| 580 | c Flux Calculation |
|---|
| 581 | c------------------------- |
|---|
| 582 | call numerical_flux_central(h,uh,z2,z,uh_l,uh_r,h_l,h_r,h_2, |
|---|
| 583 | . f_h,f_uh, em_x) |
|---|
| 584 | |
|---|
| 585 | c----------------------------------------------------- |
|---|
| 586 | c Compute time step size according to the input CFL # |
|---|
| 587 | c----------------------------------------------------- |
|---|
| 588 | 1002 dt = dmin1(factor*cfl*dx/em_x,dtmax,Tout) |
|---|
| 589 | c write(*,*)'dt = ',dt,' factor = ',factor |
|---|
| 590 | if( ( tc + dt ) .ge. Tnext ) then |
|---|
| 591 | dt = (Tnext - tc ) |
|---|
| 592 | iout = 1 |
|---|
| 593 | Tnext = Tnext+Tout |
|---|
| 594 | end if |
|---|
| 595 | if (Tnext.gt.tf ) then |
|---|
| 596 | istop = 1 |
|---|
| 597 | endif |
|---|
| 598 | |
|---|
| 599 | c------------------------------------------------- |
|---|
| 600 | c Compute the values of 'u' at the next time level |
|---|
| 601 | c------------------------------------------------- |
|---|
| 602 | ipos = 0 |
|---|
| 603 | |
|---|
| 604 | do i = md+2, md+nx |
|---|
| 605 | |
|---|
| 606 | h_new(i) = h(i) - dt/dx*( f_h(i) - f_h(i-1) ) |
|---|
| 607 | uh_new(i) = uh(i) - dt/dx*( f_uh(i) - f_uh(i-1)) |
|---|
| 608 | . - dt/dx*g*(z2(i)-z2(i-1))*(h(i)) |
|---|
| 609 | |
|---|
| 610 | if (h_new(i).lt.-1.0d-5) then |
|---|
| 611 | write(*,*)'h_new(',i,') = ',h_new(i) |
|---|
| 612 | ipos=1 |
|---|
| 613 | endif |
|---|
| 614 | |
|---|
| 615 | if (h_new(i).le.0.0d0) then |
|---|
| 616 | h_new(i) = 0.0d0 |
|---|
| 617 | c - my statement |
|---|
| 618 | uh_new(i) = 0.d0 |
|---|
| 619 | endif |
|---|
| 620 | |
|---|
| 621 | end do |
|---|
| 622 | |
|---|
| 623 | if(ipos.eq.1) then |
|---|
| 624 | factor = factor/2.0d0 |
|---|
| 625 | write(*,*)'factor = ',factor |
|---|
| 626 | goto 1002 |
|---|
| 627 | endif |
|---|
| 628 | |
|---|
| 629 | do i = md+2,nx+md |
|---|
| 630 | h(i) = h_new(i) |
|---|
| 631 | uh(i) = uh_new(i) |
|---|
| 632 | enddo |
|---|
| 633 | |
|---|
| 634 | factor = 1.0d0 |
|---|
| 635 | tc = tc + dt |
|---|
| 636 | |
|---|
| 637 | if(iout.eq.1) then |
|---|
| 638 | call util_dump_solution(h,uh,z) |
|---|
| 639 | |
|---|
| 640 | call boundary_apply(x,h,uh,z) |
|---|
| 641 | call array_limit (uh,uh_l,uh_r) |
|---|
| 642 | call array_limit_h(h,uh,z2,z,uh_l,uh_r,h_l,h_r,h_2) |
|---|
| 643 | iout = 0 |
|---|
| 644 | endif |
|---|
| 645 | if(istop.eq.1) go to 1001 |
|---|
| 646 | c |
|---|
| 647 | c End timestep |
|---|
| 648 | c |
|---|
| 649 | end do |
|---|
| 650 | c |
|---|
| 651 | 1001 write(*,*)isteps |
|---|
| 652 | |
|---|
| 653 | return |
|---|
| 654 | |
|---|
| 655 | end |
|---|
| 656 | c=========================================================== |
|---|
| 657 | c Boundary Conditions |
|---|
| 658 | c |
|---|
| 659 | c Naive Boundary Conditions |
|---|
| 660 | c Inflow, or reflective |
|---|
| 661 | c |
|---|
| 662 | c=========================================================== |
|---|
| 663 | subroutine boundary_apply(x,h,uh,z) |
|---|
| 664 | |
|---|
| 665 | implicit none |
|---|
| 666 | integer md,nxmax,nxd, mn |
|---|
| 667 | parameter (md=3, nxmax=5000, nxd=nxmax+2*md, mn=2) |
|---|
| 668 | real*8 h(nxd), uh(nxd), w(nxd) |
|---|
| 669 | real*8 z(nxd),z2(nxd) |
|---|
| 670 | real*8 x(nxd),x2(nxd) |
|---|
| 671 | |
|---|
| 672 | integer terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
|---|
| 673 | common /setup/ terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
|---|
| 674 | |
|---|
| 675 | integer nlow,nhigh,nx,nxx,dn,version,isteps |
|---|
| 676 | common /ivariables/ nlow,nhigh,nx,nxx,version,isteps |
|---|
| 677 | |
|---|
| 678 | real*8 toll,cfl,theta |
|---|
| 679 | real*8 g,hf,dx,dt,dtmax |
|---|
| 680 | real*8 Tout,tf,tc,uhf |
|---|
| 681 | real*8 K,limith,length |
|---|
| 682 | real*8 manning,hl,hr |
|---|
| 683 | common /rvariables/ toll,cfl,theta, |
|---|
| 684 | . g,hf,dx,dt,dtmax, |
|---|
| 685 | . Tout,tf,tc,uhf, |
|---|
| 686 | . K,limith,length, |
|---|
| 687 | . manning,hl,hr |
|---|
| 688 | |
|---|
| 689 | real*8 du,dh,uf,h0,u0,uh0 |
|---|
| 690 | integer ii,i |
|---|
| 691 | |
|---|
| 692 | c-------------------------------------------------- |
|---|
| 693 | |
|---|
| 694 | do i = 1, md |
|---|
| 695 | c================== |
|---|
| 696 | c Left Boundary |
|---|
| 697 | c================== |
|---|
| 698 | |
|---|
| 699 | c --- Zero |
|---|
| 700 | h(i) = 0.d0 |
|---|
| 701 | uh(i) = 0.d0 |
|---|
| 702 | end do |
|---|
| 703 | |
|---|
| 704 | do i = 1, md |
|---|
| 705 | c================== |
|---|
| 706 | c Right Boundary |
|---|
| 707 | c================== |
|---|
| 708 | |
|---|
| 709 | c --- Zero |
|---|
| 710 | h(nx+md+i) = 0.d0 |
|---|
| 711 | uh(nx+md+i) = 0.d0 |
|---|
| 712 | c h(nx+md+1) = h(nx-1) |
|---|
| 713 | c uh(nx+md+1) = uh(nx-1) |
|---|
| 714 | end do |
|---|
| 715 | |
|---|
| 716 | return |
|---|
| 717 | end |
|---|
| 718 | c=========================================================== |
|---|
| 719 | c Numerical Central Flux |
|---|
| 720 | c=========================================================== |
|---|
| 721 | subroutine numerical_flux_central(h,uh,z2,z,uh_l,uh_r,h_l,h_r, |
|---|
| 722 | . h_2,f_h,f_uh, em_x) |
|---|
| 723 | |
|---|
| 724 | implicit none |
|---|
| 725 | integer md,nxmax,nxd, mn |
|---|
| 726 | parameter (md=3, nxmax=5000, nxd=nxmax+2*md, mn=2) |
|---|
| 727 | real*8 h(nxd), uh(nxd), w(nxd) |
|---|
| 728 | real*8 z(nxd),z2(nxd) |
|---|
| 729 | real*8 x(nxd),x2(nxd) |
|---|
| 730 | |
|---|
| 731 | c integer terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
|---|
| 732 | c common /setup/ terrain,bc_l,bc_r,initial,s_h,s_uh,s_semi_uh |
|---|
| 733 | |
|---|
| 734 | integer nlow,nhigh,nx,nxx,dn,version,isteps |
|---|
| 735 | common /ivariables/ nlow,nhigh,nx,nxx,version,isteps |
|---|
| 736 | |
|---|
| 737 | real*8 toll,cfl,theta |
|---|
| 738 | real*8 g,hf,dx,dt,dtmax |
|---|
| 739 | real*8 Tout,tf,tc,uhf |
|---|
| 740 | real*8 K,limith,length |
|---|
| 741 | real*8 manning,hl,hr |
|---|
| 742 | common /rvariables/ toll,cfl,theta, |
|---|
| 743 | . g,hf,dx,dt,dtmax, |
|---|
| 744 | . Tout,tf,tc,uhf, |
|---|
| 745 | . K,limith,length, |
|---|
| 746 | . manning,hl,hr |
|---|
| 747 | |
|---|
| 748 | real*8 f_h(nxd), f_uh(nxd) |
|---|
| 749 | real*8 h_2(nxd), uh_2(nxd) |
|---|
| 750 | real*8 h_l(nxd), h_r(nxd), uh_l(nxd), uh_r(nxd) |
|---|
| 751 | |
|---|
| 752 | |
|---|
| 753 | real*8 fh_l, fuh_l, fh_r, fuh_r |
|---|
| 754 | real*8 l1_l, l2_l, l1_r, l2_r |
|---|
| 755 | real*8 a_max, a_min, aa, axa |
|---|
| 756 | |
|---|
| 757 | integer istop,iout,nt,ii,oi,i2,m,i |
|---|
| 758 | real*8 a,b,t,Tleft,em_x,dtcdx,dtcdx2,dtcdx3 |
|---|
| 759 | c real*8 den, xmt,pre, Tnext, em_old, hh |
|---|
| 760 | c real*8 aterm1 ,term1, aterm2 ,term2, aterm3 ,term3 |
|---|
| 761 | |
|---|
| 762 | c----------------------------------- |
|---|
| 763 | |
|---|
| 764 | em_x = 1.0d-15 |
|---|
| 765 | |
|---|
| 766 | do i = md,nxx-md+1 |
|---|
| 767 | |
|---|
| 768 | c |
|---|
| 769 | c ---- Calculate flux |
|---|
| 770 | c |
|---|
| 771 | |
|---|
| 772 | call flux_huh(fh_l,fuh_l,h_r(i),uh_r(i), |
|---|
| 773 | . em_x,l1_l,l2_l,g,toll) |
|---|
| 774 | call flux_huh(fh_r,fuh_r,h_l(i+1),uh_l(i+1), |
|---|
| 775 | . em_x,l1_r,l2_r,g,toll) |
|---|
| 776 | c |
|---|
| 777 | c --- Calculate max wave speed |
|---|
| 778 | c |
|---|
| 779 | a_max = dmax1(l2_l,l2_r,0.0d0) |
|---|
| 780 | a_min = dmin1(l1_l,l1_r,0.0d0) |
|---|
| 781 | c |
|---|
| 782 | c --- Compute the numerical flux |
|---|
| 783 | c |
|---|
| 784 | aa = a_max - a_min |
|---|
| 785 | axa = a_max*a_min |
|---|
| 786 | if ( aa .gt. dx*dt/1000.0d0) then |
|---|
| 787 | h_2(i) =(a_max*h_l(i+1) - a_min*h_r(i) - |
|---|
| 788 | . fh_r + fh_l )/aa |
|---|
| 789 | f_h(i) =(a_max*fh_l - a_min*fh_r + |
|---|
| 790 | . axa*(h_l(i+1)-h_r(i)))/aa |
|---|
| 791 | f_uh(i) =(a_max*fuh_l - a_min*fuh_r + |
|---|
| 792 | . axa*(uh_l(i+1)-uh_r(i)))/aa |
|---|
| 793 | else |
|---|
| 794 | h_2(i) = 0.0d0 |
|---|
| 795 | f_h(i) = 0.0d0 |
|---|
| 796 | f_uh(i) = 0.0d0 |
|---|
| 797 | endif |
|---|
| 798 | |
|---|
| 799 | enddo |
|---|
| 800 | |
|---|
| 801 | return |
|---|
| 802 | end |
|---|
| 803 | c=========================================================== |
|---|
| 804 | c Open Files |
|---|
| 805 | c=========================================================== |
|---|
| 806 | subroutine util_open_files |
|---|
| 807 | |
|---|
| 808 | open(11,file='data.w') |
|---|
| 809 | open(12,file='data.t') |
|---|
| 810 | open(13,file='data.h') |
|---|
| 811 | open(14,file='data.uh') |
|---|
| 812 | open(15,file='data.n') |
|---|
| 813 | open(16,file='data.x') |
|---|
| 814 | |
|---|
| 815 | |
|---|
| 816 | open(25,file='data.xx') |
|---|
| 817 | |
|---|
| 818 | return |
|---|
| 819 | end |
|---|
| 820 | c=========================================================== |
|---|
| 821 | c Close Files |
|---|
| 822 | c=========================================================== |
|---|
| 823 | subroutine util_close_files |
|---|
| 824 | |
|---|
| 825 | close(11) |
|---|
| 826 | close(12) |
|---|
| 827 | close(13) |
|---|
| 828 | close(14) |
|---|
| 829 | close(15) |
|---|
| 830 | close(16) |
|---|
| 831 | |
|---|
| 832 | close(25) |
|---|
| 833 | |
|---|
| 834 | return |
|---|
| 835 | end |
|---|
