conv_flux_brooks_corey.m File Reference

convective flux for Buckley-Leverett problem with Brooks-Corey functions More...

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Functions
function [ flux , lambda ] =	conv_flux_brooks_corey (glob, U, params)
	convective flux for Buckley-Leverett problem with Brooks-Corey functions More...

Detailed Description

convective flux for Buckley-Leverett problem with Brooks-Corey functions

Definition in file conv_flux_brooks_corey.m.

Function Documentation

function [ flux , lambda ] = conv_flux_brooks_corey	(		glob,
			U,
			params
	)

convective flux for Buckley-Leverett problem with Brooks-Corey functions

function computing the nonlinear convective flux of a Buckley-Leverett with Brooks-Corey approximation problem.

\[f(x,u) = \frac{\lambda_w(u)}{\lambda_w(u)+\lambda_n(u)} \quad 0\leq u \leq 1\]

.

\[\lambda_w(u) = \frac{u^{\frac{2+3\lambda}{\lambda}}}{\mu_1},\]

\[\lambda_n(u) = \frac{(1-u)^2 (1-u^{\frac{2+\lambda}{\lambda})}}{\mu_2},\]

See also

conv_flux_brooks_corey_derivative().

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().

Parameters

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

Return values

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 in decomp_mode==0, otherwise an empty variable is returned.

Required fields of params:

• bl_lambda —  mobility factor \(\lambda\)
• bl_mu1 —  viscosity of wetting phase \(\mu_1\)
• bl_mu2 —  viscosity of non-wetting phase \(\mu_2\) information
• debug —  flag indicating wether debug output shall be turned on
• decomp_mode —  flag indicating the operation mode of the function:
  • 0 (complete) : no affine parameter dependence or decomposition is performed.
  • 1 (components) : for each output argument a cell array of output matrices is returned representing the \(q\)-th component independent of the parameters given in mu_names.
  • 2 (coefficients) : returns a vector where each coordinate represents the \(q\)-the coefficient \(\sigma_{\cdot}^{q}(\mu)\) dependent on the parameters given in mu_names.

dummy

Definition at line 17 of file conv_flux_brooks_corey.m.