Relation between PVM schemes and simple Riemann solvers
type: Item
instance of: scholarly article
title: Relation between PVM schemes and simple Riemann solvers
zbMATH Open document ID: 1297.65102
author: Tomás Morales de Luna
author: Manuel Jesús Castro-Díaz
author: Carlos Parés
published in: Numerical Methods for Partial Differential Equations
publication date: 2014-08-11T00:00:00Z
Mathematics Subject Classification ID: 65M08
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 76L05
Mathematics Subject Classification ID: 35L67
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 76M12
zbMATH DE Number: 6328568
zbMATH Keywords: finite volume schemes
zbMATH Keywords: shallow water equations
zbMATH Keywords: approximate Riemann solvers
zbMATH Keywords: polynomial viscosity matrix methods
zbMATH Keywords: hyperbolic systems
zbMATH Keywords: numerical examples
describes a project that uses: PVM
describes a project that uses: GFORCE
describes a project that uses: HLLE
MaRDI profile type: Publication
full work available at URL: num.21871
OpenAlex ID: W1869625684
cites work: On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws
cites work: Numerical methods for nonconservative hyperbolic systems: a theoretical framework.
cites work: Definition and weak stability of nonconservative products
cites work: Q4680829
cites work: Semi-discrete entropy satisfying approximate Riemann solvers. The case of the Suliciu relaxation approximation
cites work: Modified Suliciu relaxation system and exact resolution of isolated shock waves
cites work: A HLLC scheme for nonconservative hyperbolic problems. Application to turbidity currents with sediment transport
cites work: A Class of Computationally Fast First Order Finite Volume Solvers: PVM Methods
cites work: Numerical approximation of hyperbolic systems of conservation laws
cites work: Polynomial upwind schemes for hyperbolic systems
cites work: Centred TVD schemes for hyperbolic conservation laws
cites work: On some fast well-balanced first order solvers for nonconservative systems
cites work: MUSTA fluxes for systems of conservation laws
cites work: On the well-balance property of Roe's method for nonconservative hyperbolic systems. applications to shallow-water systems
cites work: A weak formulation of Roe's approximate Riemann solver
cites work: NUMERICAL TREATMENT OF WET/DRY FRONTS IN SHALLOW FLOWS WITH A MODIFIED ROE SCHEME
cites work: A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
DOI: 10.1002/NUM.21871
Recommended article: On the efficient implementation of PVM methods and simple Riemann solvers. Application to the Roe method for large hyperbolic systems
Recommended article: A class of approximate Riemann solvers and their relation to relaxation schemes
Recommended article: Q5482438
Recommended article: A domain decomposition implementation of the SIMPLE method with PVM
Recommended article: Q4295519
Recommended article: Riemann-Solver Free Schemes
Recommended article: Efficient solution of the simplified \(P_N\) equations
Recommended article: Locating and computing in parallel all the simple roots of special functions using PVM
Recommended article: Approximate Riemann solvers, parameter vectors, and difference schemes. (Reprint)
Recommended article: A fast solver for riemann problems
review text: Approximate Riemann solvers (ARS) and polynomial viscosity matrix (PVM) methods constitute two general frameworks to derive numerical schemes for hyperbolic systems of partial differential equations. In this work, the relation between these two frameworks is analyzed: The authors show that every PVM method can be interpreted in terms of an approximate Riemann solver provided that it is based on a polynomial that interpolates the absolute value function at some points. Furthermore, the converse is true provided that the ARS satisfies a technical property to be specified. Besides its theoretical interest, this relation provides a useful tool to investigate the properties of some well-known numerical methods that are particular cases of PVM methods, as the analysis of some properties is easier for ARS methods. The usefulness by analyzing the positivity-preservation property is illustrated on numerical examples for the shallow water system.
reviewed by: Qin Meng Zhao
description: scientific article; zbMATH DE number 6328568