Spectral characteristics of difference schemes and conditions for numerical simulation of critical flow regimes of a viscous fluid
Abstract
A class of difference schemes approximating the NavierStokes equations for the twodimensional flow of a viscous, incompressible fluid between two infinite, parallel plates is analyzed. Conditions are established for the numerical schemes to reflect at least qualitatively the behavior of solutions to the NavierStokes equations, especially at high Reynolds numbers. The method consists in comparing the spectral characteristics of linearized NavierStokes equations with those of linearized difference equations. The closeness of these characteristics in the most important, characteristic part of the spectrum is the criterion for the qualitative accuracy of a given difference scheme.
 Publication:

Zhurnal Vychislitelnoi Matematiki i Matematicheskoi Fiziki
 Pub Date:
 December 1974
 Bibcode:
 1974ZVMMF..14.1499M
 Keywords:

 Channel Flow;
 Computerized Simulation;
 Finite Difference Theory;
 NavierStokes Equation;
 Numerical Flow Visualization;
 Two Dimensional Flow;
 Viscous Fluids;
 Algorithms;
 Critical Flow;
 Dynamic Models;
 Incompressible Fluids;
 Mathematical Models;
 Spectrum Analysis;
 Fluid Mechanics and Heat Transfer