Spurious Frequencies as a Result of Numerical Boundary Treatments

Abstract

The stability theory for finite difference Initial Boundary-Value approximations to systems of hyperbolic partial differential equations states that the exclusion of eigenvalues and generalized eigenvalues in a sufficient condition for stability. The theory, however, does not discuss the nature of numerical approximations in the presence of such eigenvalues. In fact, as was shown previously, for the problem of vortex shedding by a two dimensional cylinder in subsonic flow, stating boundary conditions in terms of the primitive (non-characteristic) variables may lead to such eigenvalues, causing perturbations that decay slowly in space and remain periodic time. Characteristic formulation of the boundary conditions avoided this problem. In this paper, we report on a more systematic study of the behavior of the (linearized) one-dimensional gas dynamic equations under various sets of oscillation-inducing legal boundary conditions. (KR)

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1990
Accession Number
ADA228536

Entities

People

  • David Gottlieb
  • Saul Abarbanel

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Layer
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Eigenvalues
  • Engineering
  • Equations
  • Euler Equations
  • Flow
  • Fluid Dynamics
  • Fluid Mechanics
  • Frequency
  • Numerical Analysis
  • Perturbations
  • Two Dimensional
  • Vortex Shedding

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Mechanics and Fluid Dynamics.

Technology Areas

  • Space