The space-time conservation element and solution element method: A new high-resolution and genuinely multidimensional paradigm for solving conservation laws
type: Item
instance of: scholarly article
title: The space-time conservation element and solution element method: A new high-resolution and genuinely multidimensional paradigm for solving conservation laws
zbMATH Open document ID: 0974.76060
author: Sin-Chung Chang
author: Xiao-Yen Wang
author: Chuen-Yen Chow
published in: Journal of Computational Physics
publication date: 2001-12-02T00:00:00Z
full work available at URL: http://hdl.handle.net/2060/19990018834
review text: The authors derive a new high-resolution and genuinely multidimensional numerical method for solving conservation laws. The method is derived using original integral form of equations, rather than their differential form. The aim is to find such a numerical scheme which is authomatically consistent with properties derived from exact integral or differential forms, e.g. with jump conditions across the shock and with the properties of characteristics. The method requires that: space and time must be treated as a single entity; both local and global flux conservation in time and space are ensured; no dimension-splitting approach is used. Specifically, the method uses a staggered space-time mesh, avoids the use of Riemann solvers, monotonicity constraints, and special techniques that are not applicable to general problems. The authors begin with a rigorous exposition of CE/SE schemes, then they evaluate their accuracy on simple scalar linear advection equation and discuss nonreflecting boundary conditions. At the end they present several numerical experiments which illustrate the robustness of the described approach.
Mathematics Subject Classification ID: 76M25
Mathematics Subject Classification ID: 76N15
Mathematics Subject Classification ID: 76L05
zbMATH DE Number: 1398866
zbMATH Keywords: space-time conservation element
zbMATH Keywords: flux conservation
zbMATH Keywords: high-resolution multidimensional method
zbMATH Keywords: conservation laws
zbMATH Keywords: shocks
zbMATH Keywords: contact discontinuities
zbMATH Keywords: scalar linear advection equation
zbMATH Keywords: nonreflecting boundary conditions
MaRDI profile type: Publication
OpenAlex ID: W1976742551
cites work: The method of space-time conservation element and solution element -- a new approach for solving the Navier-Stokes and Euler equations
cites work: Average-state Jacobians and implicit methods for compressible viscous and turbulent flows
cites work: A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
cites work: Q3994419
cites work: Computational Considerations for the Simulation of Shock-Induced Sound
cites work: Q3686255
cites work: Q4001895
cites work: Implicit total variation diminishing (TVD) schemes for steady-state calculations
cites work: High resolution schemes for hyperbolic conservation laws
cites work: A spectral element-FCT method for the compressible Euler equations
cites work: Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
cites work: The numerical simulation of two-dimensional fluid flow with strong shocks
DOI: 10.1006/JCPH.1999.6354
description: scientific article; zbMATH DE number 1398866