Cell Averaging Chebyshev Methods for Hyperbolic Problems

Abstract

This paper describes a cell averaging method for the Chebyshev approximations of first order hyperbolic equations in conservation form. We present formulas for transforming between pointwise data at the collocation points and cell averaged quantities, and vice-versa. This step, trivial for the finite difference and Fourier methods, is nontrivial for the global polynomials used in Spectral methods. We then prove that the cell averaging methods presented are stable for linear scalar hyperbolic equations and present numerical simulations of shock-density wave interaction using the new cell averaging Chebyshev methods. Keywords: Pseudospectral methods; Cell averaging techniques; Shock waves; Conservation laws.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1990
Accession Number
ADA221356

Entities

People

  • Ami Harten
  • David Gottlieb
  • Wei Cai

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Applied Mathematics
  • Boundaries
  • Boundary Value Problems
  • Cauchy Problem
  • Chebyshev Polynomials
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Differential Equations
  • Equations
  • Euler Equations
  • Identities
  • Mathematical Analysis
  • Mathematics
  • Polynomials
  • Real Variables
  • Shock Waves

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)