The Operator Compact Implicit Method for Parabolic Equations,

Abstract

This paper attempts to trace out the broad characteristics of a class of higher order finite difference schemes which are applicable to the solution of parabolic partial differential equations associated with viscous fluid flow problems. The basic method developed here uses the approach of the compact implicit techniques applied to the full spatial operator. The resulting spatial approximation, referred to here as the operator compact implicit method can be implemented with a variety of temporal integration schemes. In particular, a simple factorization technique is employed to resolve higher space dimension problems in terms of simple tridiagonal systems. The operator compact implicit method is compared to standard techniques and to some of the newer compact implicit methods. Stability characteristics, computational efficiency and the results of numerical experiments are discussed.

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Document Details

Document Type
Technical Report
Publication Date
Apr 07, 1977
Accession Number
ADA044564

Entities

People

  • Bernard C. Weinberg
  • Melvyn Ciment
  • Stephen H. Leventhal

Organizations

  • Naval Ordnance Laboratory

Tags

Communities of Interest

  • Air Platforms
  • C4I
  • Weapons Technologies

DTIC Thesaurus Topics

  • Boundary Layer
  • Boundary Layer Flow
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Differential Equations
  • Equations
  • Flow
  • Fluid Dynamics
  • Fluid Flow
  • Partial Differential Equations
  • Pressure Gradients
  • Reynolds Number
  • Steady State
  • Two Dimensional
  • Viscous Flow
  • Wave Equations

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Space