Group Velocity Interpretation of the Stability Theory of Gustafsson, Kreiss, and Sundstroem,

Abstract

The existing stability theory for finite difference models of hyperbolic initial boundary value problems, due to Gustafsson, Kreiss, and Sundstroem, is difficult to understand in its original algebraic formulation. Here we show that the GKS stability criterion has a physical interpretation in terms of group velocity: if the finite difference model together with its boundary conditions can support a set of waves at the boundary with group velocities pointing into the field, then it is unstable. A simple argument explains why such a set of waves is unstable, and yields a new theorem on what kind of unstable growth to expect. We give examples in one and two space dimensions. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1981
Accession Number
ADA111010

Entities

People

  • Lloyd N. Trefethen

Organizations

  • Stanford University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Cauchy Problem
  • Coefficients
  • Computations
  • Differential Equations
  • Dispersion Relations
  • Equations
  • Extrapolation
  • Group Velocity
  • Instability
  • Numbers
  • Numerical Analysis
  • Partial Differential Equations
  • Perturbations
  • Phase Velocity
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Geotechnical Engineering.
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space