Compact Finite Difference Schemes for Mixed Initial-Boundary Value Problems

This paper discusses a class of compact second order accurate finite difference equations for mixed initial-boundary value problems for hyperbolic and convective-diffusion equations. Convergence is proved by means of energy arguments and both types of equations are solved by similar algorithms. For...

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Bibliographic Details
Published in:SIAM journal on numerical analysis Vol. 19; no. 4; pp. 698 - 720
Main Authors: Philips, Richard B., Rose, Milton E.
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.08.1982
Subjects:
Accuracy
Algebra
Algorithms
Approximation
Boundary conditions
Boundary layers
Boundary value problems
Difference equations
Differential equations
Reynolds number
Scalars
Truncation errors
Viscosity
ISSN:0036-1429, 1095-7170
Online Access:Get full text
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Summary:This paper discusses a class of compact second order accurate finite difference equations for mixed initial-boundary value problems for hyperbolic and convective-diffusion equations. Convergence is proved by means of energy arguments and both types of equations are solved by similar algorithms. For hyperbolic equations an extension of the Lax-Wendroff method is described which incorporates dissipative boundary conditions. Upwind-downwind differencing techniques arise as the formal hyperbolic limit of the convective-diffusion equation. Finally, a finite difference "chain-rule" transforms the schemes from rectangular to quadrilateral subdomains.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0036-1429
1095-7170
DOI:10.1137/0719049