fv_num_conv_flux_lax_friedrichs.m File Reference

Function computing a numerical convective Lax-Friedrichs flux matrix. More...

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Functions
function num_flux =	fv_num_conv_flux_lax_friedrichs (model, model_data, U, NU_ind)
	Function computing a numerical convective Lax-Friedrichs flux matrix. More...

Detailed Description

Function computing a numerical convective Lax-Friedrichs flux matrix.

Definition in file fv_num_conv_flux_lax_friedrichs.m.

Function Documentation

function num_flux = fv_num_conv_flux_lax_friedrichs	(		model,
			model_data,
			U,
			NU_ind
	)

Function computing a numerical convective Lax-Friedrichs flux matrix.

Dirichlet-boundary treatment is performed, but Neumann-values are set to nan. They must be performed by the calling function.

Lax-Friedrichs-Flux

\[g_{jl}(u,v) = \frac12 (f(u,x_{jl}) + f(v,x_{jl})) \cdot \nu_{jl} - \frac{|S_{jl}|}{2 \lambda_{jl}} (v-u)\]

or equivalently

\[g_{jl}(u,v) = \frac12 |S_{jl}| \left( (f(u)+f(v)) \cdot n_{jl} - \frac{1}{\lambda_{jl}} (v-u) \right)\]

with \(\lambda_{jl} := \frac{\Delta t}{|m_j - m_l|}\).

Parameters

model	model
model_data	model data
U	U
NU_ind	NU ind

Return values

num_flux

num flux

Required fields of model:

• lxf_lambda —  (inverse of) numerical diffusion in Lax-Friedrichs flux
• flux_quad_degree —  flux quad degree
• divclean_mode —  divclean mode
• dirichlet_values_ptr —  dirichlet values ptr
• verbose —  flag indicating the verbosity level of informative output
• filecache_velocity_matrixfile_extract —  filecache velocity matrixfile extract
• conv_flux_ptr —  conv flux ptr

Required fields of model_data:

• grid —  a structure containing geometry information of a mesh used for discretizations

Generated fields of num_flux:

• Lg —  Lipschitz constant satisfying

  \[|g_{ij}(w,v) - g_{ij}(w',v')| \leq Lg |S_{ij}| ( |w'-w| + |v'-v| )\]

• G —  the matrix of numerical flux values across the edges. boundary treatment is performed as follows:
  • in dirichlet-boundary points, the neighbour-values are simply set to this value and the flux is computed.
  • Neumann-treatment is not performed here

Definition at line 17 of file fv_num_conv_flux_lax_friedrichs.m.

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