source: anuga_work/development/2010-projects/anuga_1d/sww/sww_python.py @ 7840

#! /usr/bin/python



__author__="Stephen Roberts"
__date__ ="$05/06/2010 4:54:58 PM$"


def compute_fluxes(domain):
    """Compute all fluxes and the timestep suitable for all volumes
    in domain.

    Compute total flux for each conserved quantity using "flux_function"

    Fluxes across each edge are scaled by edgelengths and summed up
    Resulting flux is then scaled by area and stored in
    explicit_update for each of the three conserved quantities
    stage, xmomentum and ymomentum

    The maximal allowable speed computed by the flux_function for each volume
    is converted to a timestep that must not be exceeded. The minimum of
    those is computed as the next overall timestep.

    Post conditions:
      domain.explicit_update is reset to computed flux values
      domain.timestep is set to the largest step satisfying all volumes.
    """

    import sys
    import numpy

    N = domain.number_of_elements

    tmp0 = numpy.zeros(N,numpy.float)
    tmp1 = numpy.zeros(N,numpy.float)

    #Shortcuts
    Stage = domain.quantities['stage']
    Xmom = domain.quantities['xmomentum']
    Bed = domain.quantities['elevation']

    #Arrays
    stage = Stage.vertex_values
    xmom =  Xmom.vertex_values
    bed =   Bed.vertex_values


    stage_bdry = Stage.boundary_values
    xmom_bdry =  Xmom.boundary_values

    flux = numpy.zeros(2, numpy.float) #Work numpy.array for summing up fluxes
    ql = numpy.zeros(2, numpy.float)
    qr = numpy.zeros(2, numpy.float)

    #Loop
    timestep = float(sys.maxint)

    for k in range(N):

        flux[:,] = 0.  #Reset work numpy.array
        #for i in range(3):
        for i in range(2):
            #Quantities inside volume facing neighbour i
            #ql[0] = stage[k, i]
            #ql[1] = xmom[k, i]
            ql = [stage[k, i], xmom[k, i]]
            zl = bed[k, i]

            #Quantities at neighbour on nearest face
            n = domain.neighbours[k,i]
            if n < 0:
                m = -n-1 #Convert negative flag to index
                qr[0] = stage_bdry[m]
                qr[1] = xmom_bdry[m]
                zr = zl #Extend bed elevation to boundary
            else:
                #m = domain.neighbour_edges[k,i]
                m = domain.neighbour_vertices[k,i]
                #print i, ' ' , m
                #qr = [stage[n, m], xmom[n, m], ymom[n, m]]
                qr[0] = stage[n, m]
                qr[1] = xmom[n, m]
                zr = bed[n, m]


            #Outward pointing normal vector
            normal = domain.normals[k, i]

            #Flux computation using provided function


            edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr)

            #print 'edgeflux', edgeflux

            # THIS IS THE LINE TO DEAL WITH LEFT AND RIGHT FLUXES
            # flux = edgefluxleft - edgefluxright
            flux -= edgeflux
            #Update optimal_timestep
            try:
                #timestep = min(timestep, 0.5*domain.radii[k]/max_speed)
                timestep = min(timestep, domain.CFL*0.5*domain.areas[k]/max_speed)
            except ZeroDivisionError:
                pass

        #Normalise by area and store for when all conserved
        #quantities get updated
        flux /= domain.areas[k]

        #Stage.explicit_update[k] = flux[0]
        tmp0[k] = flux[0]
        tmp1[k] = flux[1]


    return tmp0, tmp1


def flux_function(normal, ql, qr, zl, zr):
    """Compute fluxes between volumes for the shallow water wave equation
    cast in terms of w = h+z using the 'central scheme' as described in

    Kurganov, Noelle, Petrova. 'Semidiscrete Central-Upwind Schemes For
    Hyperbolic Conservation Laws and Hamilton-Jacobi Equations'.
    Siam J. Sci. Comput. Vol. 23, No. 3, pp. 707-740.

    The implemented formula is given in equation (3.15) on page 714

    Conserved quantities w, uh, are stored as elements 0 and 1
    in the numerical vectors ql an qr.

    Bed elevations zl and zr.
    """

    from anuga_1d.config import g, epsilon, h0
    from math import sqrt
    import numpy

    #print 'ql',ql

    #Align momentums with x-axis
    #q_left  = rotate(ql, normal, direction = 1)
    #q_right = rotate(qr, normal, direction = 1)
    q_left = ql
    q_left[1] = q_left[1]*normal
    q_right = qr
    q_right[1] = q_right[1]*normal

    #z = (zl+zr)/2 #Take average of field values
    z = 0.5*(zl+zr) #Take average of field values

    w_left  = q_left[0]   #w=h+z
    h_left  = w_left-z
    uh_left = q_left[1]

    if h_left < epsilon:
        u_left = 0.0  #Could have been negative
        h_left = 0.0
    else:
        u_left  = uh_left/(h_left +  h0/h_left)


    uh_left = u_left*h_left

    w_right  = q_right[0]  #w=h+z
    h_right  = w_right-z
    uh_right = q_right[1]


    if h_right < epsilon:
        u_right = 0.0  #Could have been negative
        h_right = 0.0
    else:
        u_right  = uh_right/(h_right + h0/h_right)

    uh_right = u_right*h_right

    #vh_left  = q_left[2]
    #vh_right = q_right[2]

    #print h_right
    #print u_right
    #print h_left
    #print u_right

    soundspeed_left  = sqrt(g*h_left)
    soundspeed_right = sqrt(g*h_right)

    #Maximal wave speed
    s_max = max(u_left+soundspeed_left, u_right+soundspeed_right, 0)

    #Minimal wave speed
    s_min = min(u_left-soundspeed_left, u_right-soundspeed_right, 0)

    #Flux computation

    #flux_left  = numpy.array([u_left*h_left,
    #                    u_left*uh_left + 0.5*g*h_left**2])
    #flux_right = numpy.array([u_right*h_right,
    #                    u_right*uh_right + 0.5*g*h_right**2])
    flux_left  = numpy.array([u_left*h_left,
                        u_left*uh_left + 0.5*g*h_left*h_left])
    flux_right = numpy.array([u_right*h_right,
                        u_right*uh_right + 0.5*g*h_right*h_right])

    denom = s_max-s_min
    if denom == 0.0:
        edgeflux = numpy.array([0.0, 0.0])
        max_speed = 0.0
    else:
        edgeflux = (s_max*flux_left - s_min*flux_right)/denom
        edgeflux += s_max*s_min*(q_right-q_left)/denom

        edgeflux[1] = edgeflux[1]*normal

        max_speed = max(abs(s_max), abs(s_min))

    return edgeflux, max_speed


if __name__ == "__main__":
    print "Hello World";