A spectral method with subcell resolution for shock wave calculations
type: Item
instance of: scholarly article
title: A spectral method with subcell resolution for shock wave calculations
zbMATH Open document ID: 0866.65065
DOI: 10.1016/0168-9274(95)00134-4
author: P. S. Crossley
author: Robert Saunders
author: D. M. Causon
author: C. G. Mingham
published in: Applied Numerical Mathematics
publication date: 1997-07-27T00:00:00Z
review text: The authors report a spectral method for the numerical solution of hyperbolic partial differential equations assuming that if discontinuous solutions occur they can be represented as the sum of a step function and a smooth function. The latter is then approximated by a series to eliminate the Gibbs phenomenon. By adding the step function to the series one obtains an accurate approximation to the solution at any given time. In this way improvements on some recently published results are reported. The method is tested on three classical problems of fluid mechanics -- the scalar wave equation, Burgers' equation and the Euler equations in gas dynamics. The accuracy of the method is illustrated by numerical examples.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 35L67
Mathematics Subject Classification ID: 76N15
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 937359
zbMATH Keywords: shock wave
zbMATH Keywords: spectral method
zbMATH Keywords: discontinuous solutions
zbMATH Keywords: Gibbs phenomenon
zbMATH Keywords: wave equation
zbMATH Keywords: Burgers' equation
zbMATH Keywords: Euler equations
zbMATH Keywords: gas dynamics
zbMATH Keywords: numerical examples
reviewed by: Nikolai L. Vulchanov
MaRDI profile type: Publication
full work available at URL: 0168-9274(95)00134-4
OpenAlex ID: W1986245676
cites work: Essentially Nonoscillatory Spectral Fourier Method for Shocks Wave Calculations
cites work: Accurate and Efficient Reconstruction of Discontinuous Functions from Truncated Series Expansions
cites work: Q4199478
cites work: ENO schemes with subcell resolution
cites work: Uniformly high order accurate essentially non-oscillatory schemes. III
cites work: Multicomponent flow calculations by a consistent primitive algorithm
cites work: Efficient implementation of essentially nonoscillatory shock-capturing schemes
cites work: A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
cites work: Convergence of Spectral Methods for Nonlinear Conservation Laws
cites work: The numerical simulation of two-dimensional fluid flow with strong shocks
description: scientific article; zbMATH DE number 937359