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conv_flux_velocity_matrixfile.m File Reference

function computing the convective flux \(f(u)\) of a convection problem. More...

Go to the source code of this file.

Functions

function [ flux
, lambda ] = 
conv_flux_velocity_matrixfile (glob, U, params)
 function computing the convective flux \(f(u)\) of a convection problem. More...
 

Detailed Description

function computing the convective flux \(f(u)\) of a convection problem.

Definition in file conv_flux_velocity_matrixfile.m.

Function Documentation

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

function computing the convective flux \(f(u)\) of a convection problem.

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
globa 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 \(f(u,x)\).
Ua vector with evaluations of a solution \(u\) which are passed as an argument to the flux function \(f\)
paramsa structure with model parameters
Return values
fluxa 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.
lambdaa 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:
  • t —  real time value in case of time-dependent flux
  • lambda —  factor for velocity computation: \(v = - \lambda \nabla p\) a velocity field is used, which is computed from an elliptic problem for the pressure by compute_pressure_gdl2() (some gdl-elements in a row, Neumann-0 and dirichlet conditions between 4 and 1 for the pressure, linear decreasing along the channel) (reasonable domain [0,1e-3] x [0,0.25e-3])
  • velocity_matrixfile —  filename of the mat-file storing the velocity field
  • 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.
Optional fields of params:
  • filecache_velocity_matrixfile_extract —  a boolean value indicating whether a cached version of the velocity field exists.
dummy

Definition at line 17 of file conv_flux_velocity_matrixfile.m.

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