conv_flux_burgers.m File Reference

function computing the convective flux of a Burgers problem. More...

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Functions
function [ flux , lambda ] =	conv_flux_burgers (glob, U, params)
	function computing the convective flux of a Burgers problem.

Detailed Description

function computing the convective flux of a Burgers problem.

Definition in file conv_flux_burgers.m.

Function Documentation

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

function computing the convective flux of a Burgers problem.

flux is a 2xnpoints matrix, representing the x/y-coordinates of the velocity in the edge midpoints.

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:

• flux_vx —  x coordinate of flux vector
• flux_vy —  y coordinate of flux vector
• flux_pdeg —  exponent \(e\) in Burgers term \(f(u) = v \cdot u^e\)
• debug —  flag indicating wether debug output shall be turned on
• verbose —  flag indicating the verbosity level of informative output

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Definition at line 17 of file conv_flux_burgers.m.