def update_solute_transport_pde(mesh,
solute_pde,
concentration_old,
v,
dt,
solute_source,
dispersion_tensor,
diffusivity,
l_disp,
t_disp,
rho_f,
verbose=False):
"""
Solve the solute transport equation.
"""
# calculate hydrodynamic dispersivity tensor from molecular diffusivity
# and longitudinal and transverse dispersivity
# calculate absolute velocity
v_abs = (v[0]**2 + v[1]**2)**0.5
# get rid of 0 values of velocity
v_abs_1 = es.whereZero(v_abs) * 1e-20 + es.whereNonZero(v_abs) * v_abs
Dxx = l_disp * (v[0]**2) / v_abs_1 + diffusivity
Dyy = t_disp * (v[1]**2) / v_abs_1 + diffusivity
# and set dispersion tensor to 0 where 0 absolute velocity
Dxx = (Dxx * es.whereNonZero(v_abs) + es.whereZero(v_abs) * diffusivity)
Dyy = (Dyy * es.whereNonZero(v_abs) + es.whereZero(v_abs) * diffusivity)
# horizontal and vertical values of dispersion (Dxx and Dyy)
dispersion_tensor[0, 0] = Dxx
dispersion_tensor[1, 1] = Dyy
# off-diagonal terms in tensor (Dxy and Dyx)
# set to 0 for now, model becomes numerically unstable
# testing with fixed values did not result in significant cahnges in solute conc...
# todo, figure out why this is unstable or check the potential error
dispersion_tensor[0, 1] = (l_disp - t_disp) * (v[0] * v[1]) / v_abs_1
dispersion_tensor[1, 0] = (l_disp - t_disp) * (v[0] * v[1]) / v_abs_1
u_old = concentration_old
a_coeff = dt * dispersion_tensor * es.kronecker(mesh)
c_coeff = dt * v
d_coeff = 1
y_coeff = u_old + solute_source * dt
if verbose is True:
print('solute transport coefficients')
print('A: ', a_coeff.getShape(), a_coeff)
print('C: ', c_coeff.getShape(), c_coeff)
print('D: ', d_coeff)
print('Y: ', y_coeff.getShape(), y_coeff)
solute_pde.setValue(A=a_coeff, C=c_coeff, D=d_coeff, Y=y_coeff)
return solute_pde
def RegionalCalculation(reg_mask):
"""
Calculates the "regional" from the entire FEILDS model excluding the
selected region and outputs gravity at the specified altitude...
see above for the "residual"
"""
# read in a gravity data grid to define data computation space
G_DATA = os.path.join(DATADIR,'Final_BouguerTC_UC15K_qrtdeg.nc')
FS=ReducedFunction(dom)
nValues=[NX, NY, 1]
first = [0, 0, cell_at_altitude]
multiplier = [1, 1, 1]
reverse = [0, 0, 0]
byteorder = BYTEORDER_NATIVE
gdata = readBinaryGrid(G_DATA, FS, shape=(),
fill=-999999, byteOrder=byteorder,
dataType=DATATYPE_FLOAT32, first=first, numValues=nValues,
multiplier=multiplier, reverse=reverse)
print("Grid successfully read")
# get the masking and units sorted out for the data-space
g_mask = whereNonZero(gdata+999999)
gdata=gdata*g_mask * GRAV_UNITS
# if people choose to have air in their region we exclude it from the
# specified gravity calculation region
if h_top < 0.:
reg_mask = reg_mask+mask_air
live_model = initial_model* whereNonPositive(reg_mask)
dead_model = initial_model* wherePositive(reg_mask)
if UseMean is True:
# calculate the mean density within the selected region
BackgroundDensity = integrate(dead_model)/integrate(wherePositive(reg_mask))
print("Density mean for selected region equals = %s"%BackgroundDensity)
live_model = live_model + BackgroundDensity * wherePositive(reg_mask)
# create mapping
rho_mapping = DensityMapping(dom, rho0=live_model)
# invert sign of gravity field to account for escript's coordinate system
gdata = -GRAV_UNITS * gdata
# turn the scalars into vectors (vertical direction)
d=kronecker(DIM)[DIM-1]
w=safeDiv(1., g_mask)
gravity_model=GravityModel(dom, w*d, gdata*d, fixPotentialAtBottom=False, coordinates=COORDINATES)
gravity_model.rescaleWeights(rho_scale=rho_mapping.getTypicalDerivative())
phi,_ = gravity_model.getArguments(live_model)
g_init = -gravity_model.getCoordinateTransformation().getGradient(phi)
g_init = interpolate(g_init, gdata.getFunctionSpace())
print("Computed gravity: %s"%(g_init[2]))
fn=os.path.join(OUTPUTDIR,'regional-gravity')
if SiloOutput is True:
saveSilo(fn, density=live_model, gravity_init=g_init, g_initz=-g_init[2], gravitymask=g_mask, modelmask=reg_mask)
print('SILO file written with the following fields: density (kg/m^3), gravity vector (m/s^2), gz (m/s^2), gravitymask, modelmask')
# to compare calculated data against input dataset.
# Not used by default but should work if the input dataset is correct
#gslice = g_init[2]*wherePositive(g_mask)
#g_dash = integrate(gslice)/integrate(wherePositive(g_mask))
#gdataslice = gdata*wherePositive(g_mask)
#gdata_dash = integrate(gdataslice)/integrate(wherePositive(g_mask))
#misfit=(gdataslice-gdata_dash)-(gslice-g_dash)
saveDataCSV(fn+".csv", mask=g_mask, gz=-g_init[2], Long=datacoords[0], Lat=datacoords[1], h=datacoords[2])
print('CSV file written with the following fields: Longitude (degrees) Latitude (degrees), h (100km), gz (m/s^2)')
pass
# read in the FEILDS Voxet
initial_model = readVoxet(dom, MODEL_DATASET, MODEL_PROPERTY, MODEL_ORIGIN,
0., COORDINATES)
# set the extents of the desired "region" for clipping and computation,
# mask is = 1 OUTSIDE area of interest
mask_air = whereNonNegative(dom.getX()[2]+spacing[2]/2) #reg_mask for air layer
mask_LONG = wherePositive(Longitude_W-datacoords[0]) + whereNegative(Longitude_E-datacoords[0]) #reg_mask for longitude
mask_LAT = whereNegative(Latitude_N-datacoords[1]) + wherePositive(Latitude_S-datacoords[1]) #reg_mask for latitude
mask_h = wherePositive(datacoords[2]+(h_top/100)) + whereNegative(datacoords[2]+(h_base/100)) #reg_mask for depth
if ReverseSelection:
reg_mask = whereNonZero(mask_LONG+mask_LAT+mask_h)
else:
reg_mask = whereZero(mask_LONG+mask_LAT+mask_h)
# prior to any computation, write out the selected region model as CSV
# and Silo if requested
fn = os.path.join(OUTPUTDIR, "region_%s")%(MODEL_PROPERTY)
saveDataCSV(fn+".csv", Long=datacoords[0], Lat=datacoords[1], h=datacoords[2],
PROPERTY=initial_model, mask=reg_mask)
print("CSV file written with the following fields: Longitude (degrees)"
+" Latitude (degrees), h (100km), Property (kg/m^3 or Pa)")
if SiloOutput:
saveSilo(fn, PROPERTY=initial_model, mask=reg_mask)
print('SILO file written with the following fields: Property (kg/m^3 or Pa), mask')