A comparative study of advanced shock-capturing schemes applied to Burgers' equation
type: Item
instance of: scholarly article
title: A comparative study of advanced shock-capturing schemes applied to Burgers' equation
zbMATH Open document ID: 0759.76053
DOI: 10.1016/S0021-9991(05)80012-9
author: S. Singh
published in: Journal of Computational Physics
publication date: 1992-10-12T00:00:00Z
review text: We have considered several variations of the TVD and FCT schemes and geometrical approaches such as MUSCL, ENO, and PPM. Included is an organized overview and classification of the schemes. Only essential features are described, and numerical implementation is discussed. Much of the mathematical theory is omitted, but a key source reference list is provided. We present a comparative study of these schemes applied to the Burgers' equation. The objective is to assess their performance for problems involving formation and propagation of shocks, shock collisions, and expansion of discontinuities.
Mathematics Subject Classification ID: 76M20
Mathematics Subject Classification ID: 76L05
zbMATH DE Number: 69163
zbMATH Keywords: TVD and FCT schemes
zbMATH Keywords: MUSCL
zbMATH Keywords: ENO
zbMATH Keywords: PPM
zbMATH Keywords: shock collisions
zbMATH Keywords: expansion of discontinuities
MaRDI profile type: Publication
cites work: High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws
cites work: High resolution schemes for hyperbolic conservation laws
cites work: Implicit total variation diminishing (TVD) schemes for steady-state calculations
cites work: Construction of explicit and implicit symmetric TVD schemes and their applications
cites work: Fully multidimensional flux-corrected transport algorithms for fluids
cites work: High-order upwind flux correction methods for hyperbolic conservation laws
cites work: Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
cites work: A Geometric Approach to High Resolution TVD Schemes
cites work: Simplified Second-Order Godunov-Type Methods
cites work: A Direct Eulerian MUSCL Scheme for Gas Dynamics
cites work: The piecewise parabolic method (PPM) for gas-dynamical simulations
cites work: Flux-corrected transport. I: SHASTA, a fluid transport algorithm that works
cites work: Flux-corrected transport. II: Generalizations of the method
cites work: High order ''ZIP'' differencing of convective terms
cites work: TVB Uniformly High-Order Schemes for Conservation Laws
cites work: Efficient implementation of essentially nonoscillatory shock-capturing schemes
cites work: A Random Choice Finite Difference Scheme for Hyperbolic Conservation Laws
full work available at URL: s0021-9991(05)80012-9
OpenAlex ID: W2029544660
description: scientific article; zbMATH DE number 69163