Time-Stable Boundary Conditions for Finite-Difference Schemes Solving Hyperbolic Systems: Methodology and Application to High-Order Compact Schemes

Abstract

We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Pade-like) high-order finite-difference schemes for hyperbolic systems. First a proper summation-by-parts formula is found for the approximate derivative. A simultaneous approximation term (SAT) is then introduced to treat the boundary conditions. This procedure leads to time-stable schemes even in the system case. An explicit construction of the fourth-order compact case is given. Numerical studies are presented to verify the efficacy of the approach.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1993
Accession Number
ADA262950

Entities

People

  • David Gottlieb
  • Mark H. Carpenter
  • Saul Abarbanel

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Applied Mathematics
  • Boundaries
  • Computational Fluid Dynamics
  • Computational Science
  • Convergence
  • Differential Equations
  • Eigenvalues
  • Engineering
  • Equations
  • Errors
  • Fluid Mechanics
  • Guarantees
  • Mathematics
  • Partial Differential Equations
  • Polynomials
  • Truncation
  • Wave Equations

Fields of Study

  • Mathematics

Readers

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