Paper Info
Title
Constraint Preserving Schemes Using Potential-Based Fluxes. II. Genuinely Multidimensional Systems of Conservation Laws
Abstract
We introduce a class of numerical schemes that preserve a discrete version of vorticity in conservation laws which involve grad advection. These schemes are based on reformulating finite volume schemes in terms of vertex centered numerical potentials. The resulting potential-based schemes have a genuinely multidimensional structure. A suitable choice of potentials leads to discrete vorticity preserving schemes that are simple to code, computationally inexpensive, and proven to be stable. We extend our discussion to other classes of genuinely multidimensional schemes. Numerical examples for linear grad advection equations, linear and nonlinear wave equation systems, and the Euler equations of gas dynamics are presented.
Year
DOI
Venue
2011
10.1137/090770138
SIAM J. Numerical Analysis
Keywords
Field
DocType
genuinely multidimensional systems,potential-based fluxes,linear grad advection equation,genuinely multidimensional structure,genuinely multidimensional scheme,numerical potential,grad advection,euler equation,conservation laws,discrete version,constraint preserving,numerical scheme,numerical example,discrete vorticity,conservation law,multidimensional system
Mathematical optimization,Gas dynamics,Vorticity,Vertex (geometry),Mathematical analysis,Advection,Euler equations,Finite volume method,Mathematics,Conservation law,Multidimensional systems
Journal
Volume
Issue
ISSN
49
3
0036-1429
Citations 
PageRank 
References 
3
0.53
7
Authors
2
Name
Order
Citations
PageRank
Siddhartha Mishra117021.36
Eitan Tadmor2796163.63