A two-point difference scheme for computing steady-state solutions to the conservative one-dimensional Euler equations
type: Item
instance of: scholarly article
title: A two-point difference scheme for computing steady-state solutions to the conservative one-dimensional Euler equations
zbMATH Open document ID: 0563.76023
DOI: 10.1016/0045-7930(84)90024-0
author: Stephen Wornom
published in: Computers and Fluids
publication date: 1984-01-01T00:00:00Z
review text: An implicit finite-difference method is presented for obtaining steady- state solutions to the time dependent Euler equations, written in the conservation form, for flow containing shocks. The method uses a two- difference scheme for flux derivatives at subsonic points, at supersonic points, dissipation is added by retarded density concept, and the difference equations involve three points. However, the overall method retains the nice feature of the general two-point method as regards boundary conditions. Application of the method to quasi-one-dimensional nozzle flow equations is introduced for five different test cases, combining subsonic and supersonic boundary conditions. Some comparison with three-point method is made. Calculated results show the method's advantages. Residuals can be reduced to machine zero in approximately 35 time steps for 50 mesh points. For one-dimensional Euler calculations, the scheme offers two advantages; the first is in regard to application of boundary conditions, the second is that the two-point algorithm is well-conditioned for large time steps.
Mathematics Subject Classification ID: 76B99
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 3898431
zbMATH Keywords: implicit finite-difference method
zbMATH Keywords: steady-state solutions
zbMATH Keywords: time dependent Euler equations
zbMATH Keywords: flow containing shocks
zbMATH Keywords: dissipation
zbMATH Keywords: retarded density concept
zbMATH Keywords: two-point method
zbMATH Keywords: quasi-one-dimensional nozzle flow
MaRDI profile type: Publication
full work available at URL: 0045-7930(84)90024-0
OpenAlex ID: W2021337859
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description: scientific article; zbMATH DE number 3898431