An Implicit Numerical Method for the Multidimensional Compressible Navier-Stokes Equations.

Abstract

In an effort to exploit the favorable stability properties of implicit methods and thereby increase computational efficiency by taking large time steps, an implicit finite-difference method for the multidimensional Navier-Stokes equations is presented. The method is based on a fully-implicit backward time difference scheme which is linearized by Taylor expansion about the known time level to produce a set of coupled linear difference equations which are valid for a given time step. To solve these difference equations, the Douglas-Gunn procedure for generating alternating-direction implicit (ADI) schemes as perturbations of fundamental implicit difference schemes is introduced. The resulting sequence of one-dimensional equations can be solved efficiently by standard block-elimination methods. The method is a one-step method, as opposed to a predictor-corrector method, and requires no iteration to compute the solution for a single time step. The stability and accuracy of the method are examined in a three-dimensional application to subsonic flow in a straight duct with rectangular cross section. (Modified author abstract)

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1973
Accession Number
AD0770224

Entities

People

  • Henry Mcdonald
  • W. Roger Briley

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Accuracy
  • Difference Equations
  • Differential Equations
  • Efficiency
  • Elimination
  • Equations
  • Flow
  • Iterations
  • Mathematical Analysis
  • Mathematics
  • Navier Stokes Equations
  • Numerical Analysis
  • Perturbations
  • Subsonic Flow
  • Three Dimensional

Readers

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