Upwind finite-volume method with a triangular mesh for conservation laws

Research output: Contribution to journalArticle

Abstract

A new upwind scheme has been developed and analyzed for a finite-volume solution of the conservation laws on triangular meshes. The scheme is an upwind second-order extrapolation with simple local limiters, and it is weakly second-order accurate and satisfies maximum principles. In one dimension, the scheme reduces to a fully upwind second-order scheme with a simple local limiter. Preliminary numerical results demonstrating the performance of the scheme on a variety of initial-boundary value problems are presented. The order of convergence of the scheme is found to vary from 1.6 to 1.9 in L1 .

Original language English 324-337 14 Journal of Computational Physics 107 2 https://doi.org/10.1016/jcph.1993.1147 Published - 1993 Jan 1

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maximum principle
Triangular Mesh
finite volume method
Limiters
Finite volume method
conservation laws
Finite Volume Method
boundary value problems
Conservation Laws
extrapolation
mesh
Conservation
Maximum principle
Extrapolation
Limiter
Boundary value problems
Upwind Scheme
Order of Convergence
Maximum Principle
Finite Volume

All Science Journal Classification (ASJC) codes

• Numerical Analysis
• Modelling and Simulation
• Physics and Astronomy (miscellaneous)
• Physics and Astronomy(all)
• Computer Science Applications
• Computational Mathematics
• Applied Mathematics

Cite this

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title = "Upwind finite-volume method with a triangular mesh for conservation laws",
abstract = "A new upwind scheme has been developed and analyzed for a finite-volume solution of the conservation laws on triangular meshes. The scheme is an upwind second-order extrapolation with simple local limiters, and it is weakly second-order accurate and satisfies maximum principles. In one dimension, the scheme reduces to a fully upwind second-order scheme with a simple local limiter. Preliminary numerical results demonstrating the performance of the scheme on a variety of initial-boundary value problems are presented. The order of convergence of the scheme is found to vary from 1.6 to 1.9 in L1 .",
author = "San-Yih Lin",
year = "1993",
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journal = "Journal of Computational Physics",
issn = "0021-9991",
publisher = "Academic Press Inc.",
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}

In: Journal of Computational Physics, Vol. 107, No. 2, 01.01.1993, p. 324-337.

Research output: Contribution to journalArticle

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N2 - A new upwind scheme has been developed and analyzed for a finite-volume solution of the conservation laws on triangular meshes. The scheme is an upwind second-order extrapolation with simple local limiters, and it is weakly second-order accurate and satisfies maximum principles. In one dimension, the scheme reduces to a fully upwind second-order scheme with a simple local limiter. Preliminary numerical results demonstrating the performance of the scheme on a variety of initial-boundary value problems are presented. The order of convergence of the scheme is found to vary from 1.6 to 1.9 in L1 .

AB - A new upwind scheme has been developed and analyzed for a finite-volume solution of the conservation laws on triangular meshes. The scheme is an upwind second-order extrapolation with simple local limiters, and it is weakly second-order accurate and satisfies maximum principles. In one dimension, the scheme reduces to a fully upwind second-order scheme with a simple local limiter. Preliminary numerical results demonstrating the performance of the scheme on a variety of initial-boundary value problems are presented. The order of convergence of the scheme is found to vary from 1.6 to 1.9 in L1 .

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