A wave propagation method for three-dimensional hyperbolic conservation laws
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In this article, a class of wave propagation algorithms for three-dimensional conservation laws and other hyperbolic systems is developed, which are based on solving one-dimensional Riemann problems at the cell interfaces and applying flux-limiter functions to suppress oscillations arising from second-derivative terms.About:
This article is published in Journal of Computational Physics.The article was published on 2000-11-20 and is currently open access. It has received 122 citations till now. The article focuses on the topics: Riemann problem & Euler equations.read more
Citations
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An unsplit Godunov method for ideal MHD via constrained transport
TL;DR: A single step, second-order accurate Godunov scheme for ideal MHD based on combining the piecewise parabolic method for performing spatial reconstruction, the corner transport upwind method of Colella for multidimensional integration, and the constrained transport (CT) algorithm for preserving the divergence-free constraint on the magnetic field is described.
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An unsplit Godunov method for ideal MHD via constrained transport in three dimensions
TL;DR: This paper describes the calculation of the PPM interface states for 3D ideal MHD which must include multidimensional ''MHD source terms'' and naturally respect the balance implicit in these terms by the @?B=0 condition and compares two different forms for the CTU integration algorithm.
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Adaptive Mesh Refinement Using Wave-Propagation Algorithms for Hyperbolic Systems
Marsha Berger,Randall J. LeVeque +1 more
TL;DR: An adaptive mesh refinement algorithm developed for the Euler equations of gas dynamics has been extended to employ high-resolution wave-propagation algorithms in a more general framework, including hyperbolic equations not in conservation form, problems with source terms or capacity functions, and logically rectangular curvilinear grids.
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A Wave Propagation Method for Conservation Laws and Balance Laws with Spatially Varying Flux Functions
Derek S. Bale,Randall J. LeVeque +1 more
TL;DR: A high-resolution wave-propagation algorithm is defined in which waves are based directly on a decomposition of flux differences fi( Qi)-f-1(Qi-1) into eigenvectors of an approximate Jacobian matrix and is shown to be second-order accurate for smooth problems and allows the application of wave limiters to obtain sharp results on discontinuities.
Journal ArticleDOI
Tsunami modelling with adaptively refined finite volume methods
TL;DR: These issues are discussed in the context of Riemann-solver-based finite volume methods for tsunami modelling in a ‘wellbalanced’ manner and also apply to a variety of other geophysical flows.
References
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Journal ArticleDOI
Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes
TL;DR: In this article, it is shown that these features can be obtained by constructing a matrix with a certain property U, i.e., property U is a property of the solution of the Riemann problem.
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Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method
TL;DR: In this article, a second-order extension of the Lagrangean method is proposed to integrate the equations of ideal compressible flow, which is based on the integral conservation laws and is dissipative, so that it can be used across shocks.
Book
Riemann Solvers and Numerical Methods for Fluid Dynamics
TL;DR: In this article, the authors present references and index Reference Record created on 2004-09-07, modified on 2016-08-08 and a reference record created on 2003-09 -07.
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The Piecewise Parabolic Method (PPM) for Gas Dynamical Simulations
Phillip Colella,Paul R. Woodward +1 more
TL;DR: This work recognizes the need for additional dissipation in any higher-order Godunov method of this type, and introduces it in such a way so as not to degrade the quality of the results.
Book
Numerical methods for conservation laws
TL;DR: In this paper, the authors describe the derivation of conservation laws and apply them to linear systems, including the linear advection equation, the Euler equation, and the Riemann problem.