Marching iterative methods for the Parabolized and Thin Layer NavierStokes equations
Abstract
Downstream marching iterative schemes for the solution of the Parabolized or Thin Layer (PNS or TL) NavierStokes equations are described. Modifications of the primitive equation global relaxation sweep procedure result in efficient secondorder marching schemes. These schemes take full account of the reduced order of the approximate equations as they behave like the SLOR for a single elliptic equation. The improved smoothing properties permit the introduction of MultiGrid acceleration. The proposed algorithm is essentially Reynolds number independent and therefore can be applied to the solution of the subsonic Euler equations. The convergence rates are similar to those obtained by the MultiGrid solution of a single elliptic equation; the storage is also comparable as only the pressure has to be stored on all levels. Extensions to threedimensional and compressible subsonic flows are discussed. Numerical results are presented.
 Publication:

IN: Progress and supercomputing in computational fluid dynamics; Proceedings of U.S.Israel Workshop
 Pub Date:
 1985
 Bibcode:
 1985pscf.proc..211I
 Keywords:

 Approximation;
 Euler Equations Of Motion;
 Iterative Solution;
 NavierStokes Equation;
 Relaxation Method (Mathematics);
 Time Marching;
 Compressible Flow;
 Computational Fluid Dynamics;
 Problem Solving;
 Three Dimensional Flow;
 Fluid Mechanics and Heat Transfer