The characteristic-Galerkin method for advection-dominated problems - An assessment
type: Item
instance of: scholarly article
title: The characteristic-Galerkin method for advection-dominated problems - An assessment
zbMATH Open document ID: 0611.76095
DOI: 10.1016/0045-7825(87)90100-9
author: Oleg C. Zienkiewicz
author: Joseph H. W. Lee
author: Jaime Peraire
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1987-01-01T00:00:00Z
review text: We present results of an accuracy analysis of a recent characteristic- based Galerkin method suited for advection-dominated problems. The analysis shows that the numerical propagation characteristics of the explicit time-stepping scheme which uses linear basis functions for spatial discretization are superior to those of the related classical Lax-Wendroff method and the implicit Crank-Nicolson scheme. The model is subjected to three analytical test problems which embrace many essential realistic features of environmental and coastal hydrodynamic applications: pure advection of a steep Gaussian profile, dispersion of a continuous source in an oscillating flow, and long-wave propagation with bottom frictional dissipation in a rectangular channel. The numerical results demonstrate that the accuracy achieved with the present scheme is excellent and comparable to that of a characteristic- based finite difference scheme which uses Hermitian cubic interpolating polynomials. The results reported herein suggest strongly further use and testing of this robust model in engineering practice.
Mathematics Subject Classification ID: 76R50
Mathematics Subject Classification ID: 76M99
Mathematics Subject Classification ID: 86A05
zbMATH DE Number: 3988990
zbMATH Keywords: one-dimensional convective diffusion equation
zbMATH Keywords: accuracy analysis
zbMATH Keywords: characteristic-based Galerkin method
zbMATH Keywords: advection-dominated problems
zbMATH Keywords: numerical propagation characteristics
zbMATH Keywords: explicit time-stepping scheme
zbMATH Keywords: linear basis functions
zbMATH Keywords: spatial discretization
zbMATH Keywords: classical Lax-Wendroff method
zbMATH Keywords: implicit Crank-Nicolson scheme
zbMATH Keywords: coastal hydrodynamic applications
zbMATH Keywords: pure advection
zbMATH Keywords: steep Gaussian profile
zbMATH Keywords: dispersion of a continuous source
zbMATH Keywords: oscillating flow
zbMATH Keywords: long-wave propagation
zbMATH Keywords: bottom frictional dissipation
zbMATH Keywords: rectangular channel
zbMATH Keywords: characteristic-based finite difference scheme
zbMATH Keywords: Hermitian cubic interpolating polynomials
MaRDI profile type: Publication
full work available at URL: 0045-7825(87)90100-9
OpenAlex ID: W1983695232
cites work: Q3707286
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description: scientific article; zbMATH DE number 3988990