Balancing Source Terms and Flux Gradients in High-Resolution Godunov Methods: The Quasi-Steady Wave-Propagation Algorithm

Balancing Source Terms and Flux Gradients in High-Resolution Godunov Methods: The Quasi-Steady Wave-Propagation Algorithm (1998)

by Randall J. Leveque

Venue:	J. Comput. Phys
Citations:	39 - 5 self

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Datum	Value	Source
TITLE	Balancing Source Terms and Flux Gradients in High-Resolution Godunov Methods: The Quasi-Steady Wave-Propagation Algorithm	user correction - Legacy Corrections
AUTHOR NAME	Randall J. Leveque	SVM HeaderParse 0.2
AUTHOR AFFIL	1	SVM HeaderParse 0.2
ABSTRACT	. Conservation laws with source terms often have steady states in which the flux gradients are nonzero but exactly balanced by source terms. Many numerical methods (e.g., fractional step methods) have difficulty preserving such steady states and cannot accurately calculate small perturbations of such states. Here a variant of the wave-propagation algorithm is developed which addresses this problem by introducing a Riemann problem in the center of each grid cell whose flux difference exactly cancels the source term. This leads to modified Riemann problems at the cell edges in which the jump now corresponds to perturbations from the steady state. Computing waves and limiters based on the solution to these Riemann problems gives high-resolution results. The 1D and 2D shallow water equations for flow over arbitrary bottom topography are use as an example, though the ideas apply to many other systems. The method is easily implemented in the software package clawpack. Keywords: Godunov meth...	user correction - Legacy Corrections
YEAR	1998	INFERENCE
VENUE	J. Comput. Phys	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	346--365	INFERENCE
VOLUME	146	INFERENCE
CITATIONS	25 found	ParsCit 1.0