Convergence of Generalized MUSCL Schemes

TLDR: Semidiscrete generalizations of the second order extension of Godunov’s scheme, known as the MUSCL scheme, are constructed, starting with any three point “E” scheme, used to approximate scalar conservation laws in one space dimension.

Abstract: Semidiscrete generalizations of the second order extension of Godunov’s scheme, known as the MUSCL scheme, are constructed, starting with any three point “E” scheme. They are used to approximate scalar conservation laws in one space dimension. For convex conservation laws, each member of a wide class is proven to be a convergent approximation to the correct physical solution. Comparison with another class of high resolution convergent schemes is made.

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NASA ContractorReport172306
1C ASE 1NAsS40A;1CR2_872306
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CONVERGENCE OF GENERALIZED MUSCL SCHEMES
Stanley Osher
Contract No. NASI-17070
February 1984
INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING
NASA Langley Research Center, Hampton, Virginia 23665
Operated by the Universities Space Research Association
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Space Administration L',!"_Lr:;' RE_E,r.RC:4,;ErJr_R
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Langley Research Center H.,_.:,q-on,V=R_r't._,
Hampton, Virginia 23665

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3 117 62
CONVERGENCEOFGENERALIZEDM_SCL SCHEMES
Stanley Osher
University of California
Los Angeles
Abstract
Semi-discrete generalizations of the second order extension of Godunov's
scheme, known as the MUSCL scheme, are constructed, starting with any three
point "E" scheme. They are used to approximate scalar conservation laws in
one space dimension. For convex conservation laws, each member of a wide
class is proven to be a convergent approximation to the correct physical
solution. Comparison with another class of high resolution convergent schemes
is made.
Research supported in part by NSF Grant No. MCS 82-00788, ARO Grant No.
DAAG 29-82-k-0090, and NASA Grant No. NAG-I-270. Part of the research was
carried out while the author was a visitor at the Institute for Computer
Applications in Science and Engineering (ICASE), NASA Langely Research Center,
Hampton, VA., which is operated under NASA Contract No. NASI-17070.
i

Frequently asked questions

Q1. What are the contributions in this paper?

Part of the research was carried out while the author was a visitor at the Institute for Computer Applications in Science and Engineering ( ICASE ), NASA Langely Research Center, Hampton, VA., which is operated under NASA Contract No. NASI-17070.