Numerical solution of the complete NavierStokes equations for the simulation of unsteady flows
Abstract
An extremely stable 'fully' implicit finitedifference method is described in detail. Although unconditional stability for the complete nonlinear equations has not been proved, it can be assumed that for stability the timestep restriction is less severe than for equivalent explicit or weakly implicit schemes. This aspect is particularly important for the simulation of strongly unsteady flows at high Reynolds numbers where it is desirable that the time step be adjusted with respect to the physical requirements of the unsteady flow variation rather than to satisfy a stability criterion. Some typical results obtained with this method are presented; they are results of calculations for a boundary layer flow and a plane Poiseuille flow disturbed periodically at the inflow boundary.
 Publication:

Approximation Methods for NavierStokes Problems
 Pub Date:
 1980
 Bibcode:
 1980appm.proc..177F
 Keywords:

 Computational Fluid Dynamics;
 Finite Difference Theory;
 Mathematical Models;
 NavierStokes Equation;
 Unsteady Flow;
 Boundary Layer Flow;
 Boundary Value Problems;
 Laminar Flow;
 Nonlinear Equations;
 Numerical Stability;
 Reynolds Number;
 Fluid Mechanics and Heat Transfer