Boundary Conditions for Suppressing Rapidly Moving Components in Hyperbolic Systems. I.

Abstract

This work is concerned with hyperbolic systems of partial differential equations for which certain of the associated propagation speeds are a great deal larger than the other proposition speeds. Our goal is to find boundary conditions which prevent rapidly moving waves from entering the given spatial domain. Conditions of this type are desirable in certain numerical computations arising in meteorology. In order to find these conditions, we first transform the given system to an approximate diagonal form in such a way that each of the new dependent variables can be identified as a slow, incoming fast, or outgoing fast component of the solution. we then find local boundary conditions which suppress the incoming fast part. Pseudo-differential operators are used throughout the entire process. We consider only linear systems. In Part II of this work (7) these methods are applied in detail to the linearized shallow water equations. The results of numerical tests of various boundary conditions are included in both papers. We also outline a method by which the conditions can be justified analytically. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1982
Accession Number
ADA120962

Entities

People

  • Robert L. Higdon

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Eigenvalues
  • Equations
  • Euler Equations
  • Formulas (Mathematics)
  • Gas Dynamics
  • Grids
  • Mathematics
  • Military Research
  • Notation
  • Partial Differential Equations
  • Shallow Water
  • Ultrasounds
  • United States
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Linear Algebra
  • Systems Analysis and Design