Solution of the Multidimensional Compressible Navier-Stokes Equations by a Generalized Implicit Method
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 consists of a generalized implicit scheme which has been linearized by Taylor expansion about the solution at 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 employed. The resulting sequence of narrow block-banded systems 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 use of both second and fourth order spatial differencing is discussed. Test calculations are presented for a three- dimensional application to subsonic flow in a straight duct with rectangular cross section.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1976
- Accession Number
- ADA020554
Entities
People
- H. J. Gibeling
- H. Mcdonald
- W. R. Briley
Organizations
- United Technologies Corporation