convective flux for Buckley-Leverett problem More...
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Functions | |
function [
flux , lambda ] = | conv_flux_buckley_leverett (glob, U, params) |
convective flux for Buckley-Leverett problem More... | |
convective flux for Buckley-Leverett problem
Definition in file conv_flux_buckley_leverett.m.
function [ flux , lambda ] = conv_flux_buckley_leverett | ( | glob, | |
U, | |||
params | |||
) |
convective flux for Buckley-Leverett problem
function computing the nonlinear convective flux of a Buckley-Leverett problem.
\[f(x,u) = \frac{u^2}{u^2+ M (1-u^2)} \quad 0\leq u \leq 1\]
.
Convective flux functions are used e.g. by finite folume operators like fv_operators_conv_explicit_lax_friedrichs() or fv_num_conv_flux_engquist_osher().
glob | a matrix of row vectors for each coordinate dimension of the grid defining the coordinates where the flux function is evaluated, in case it is space dependent, i.e. we have something like \(f(u,x)\). |
U | a vector with evaluations of a solution \(u\) which are passed as an argument to the flux function \(f\) |
params | a structure with model parameters |
flux | a matrix which entries \(F_{ji}\) represent the \(i\)-th component of the flux vector \(f(u(x_{j}))\) in the edge midpoint \(x_{j}\) given by the glob argument. |
lambda | a bound such that \[\lambda \cdot \sup_u n_{jl} \cdot f'(u) \leq 1\] e.g. \(\lambda := \frac{1}{\sup|v(x,y)|}\) for \(f(u) = v \cdot u\). This is value only reasonable indecomp_mode==0 , otherwise an empty variable is returned. |
bl_k —
scaling factor for flux bl_M —
steepness factor of curve. U —
DoF vector of discrete solution grid —
pointer to grid structure for neighbour information debug —
flag indicating wether debug output shall be turned on conv_a —
conv a decomp_mode —
flag indicating the operation mode of the function:mu_names
.mu_names
.Definition at line 17 of file conv_flux_buckley_leverett.m.