The Instability of Numerical Boundary Treatments for Compact High-Order Finite-Difference Schemes

Abstract

The stability characteristics of various compact fourth- and sixth- order spatial operators are assessed using the theory of Gustafsson, Kreiss and Sundstrom (G-K-S) for the semi-discrete Initial Boundary Value Problem (IBVP). These results are then generalized to the fully discrete case using a recently developed theory of Kreiss. In all cases, favorable comparisons are obtained between G-K-S theory, eigenvalue determination, and numerical simulation. The conventional definition of stability is then sharpened to include only those spatial discretizations that are asymptotically stable (bounded, Left Half-Plane eigenvalues). It is shown that many of the higher-order schemes which are G-K-S stable are not asymptotically stable. A series of compact fourth- and sixth- order schemes, which are both asymptotically and G-K-S stable for the scalar case, are then developed.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1991
Accession Number
ADA241939

Entities

People

  • David Gottlieb
  • Mark H. Carpenter
  • Saul Abarbanel

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Cauchy Problem
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Eigenvalues
  • Engineering
  • Equations
  • Navier Stokes Equations
  • Numerical Analysis
  • Partial Differential Equations
  • Simulations
  • Theorems
  • Wave Equations

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)