Spectral Methods: Analysis and Applications to Flow Problems.

Abstract

In this paper, we have shown that we can characterize methods for the solution of incompressible flow problems as belonging to either parabolic or elliptic type with regard to the determination of pressure field. The elliptic schemes typically have smaller errors in the divergence field, with the errors decaying exponentially away from the boundaries of the computational domain. On the other hand, the parabolic schemes have smooth solutions, without numerical boundary layers, but care should be exercised with respect to the boundary conditions in order that initial divergence errors be eliminated. This analysis explains why elliptic schemes, like that introduced by Harlow Welch (1965) have been found to be more accurate than parabolic schemes.

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Document Details

Document Type
Technical Report
Publication Date
Dec 22, 1986
Accession Number
ADA186265

Entities

People

  • David Gottlieb

Organizations

  • Universities Space Research Association

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Boundaries
  • Boundary Layer
  • Compressible Flow
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Eigenvectors
  • Equations
  • Errors
  • Euler Equations
  • Flow
  • Fluid Dynamics
  • Incompressible Flow
  • Partial Differential Equations

Fields of Study

  • Mathematics

Readers

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