Accurate Finite Difference Methods for Time-Harmonic Wave Propagation

Abstract

Finite difference methods for solving problems of time-harmonic acoustics are developed and analyzed. Multi-dimensional inhomogeneous problems with variable, possibly discontinuous, coefficients are considered, accounting for the effects of employing non-uniform grids. A weighted-average representation is less sensitive to transition in wave resolution (due to variable wave numbers or non-uniform grids) than the standard pointwise representation. Further enhancement in method performance is obtained by basing the stencils on generalizations of Pade approximation, or generalized definitions of the derivative, reducing spurious dispersion, anisotropy and reflection, and by improving the representation of source terms. The resulting schemes have fourth-order accurate local truncation error on uniform grids and third order in the non-uniform case. Guidelines for discretization pertaining to grid orientation and resolution are presented. Helmholtz equation, High order scheme

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1994
Accession Number
ADA279019

Entities

People

  • Eli Turkel
  • Isaac Harari

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Anisotropy
  • Coefficients
  • Difference Equations
  • Differential Equations
  • Dispersion Relations
  • Dispersions
  • Equations
  • Errors
  • Group Velocity
  • Helmholtz Equations
  • Orientation (Direction)
  • Phase Velocity
  • Physical Properties
  • Reflection
  • Two Dimensional
  • Wave Propagation

Readers

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