A timeaccurate, unsteady, incompressible NavierStokes CFD algorithm
Abstract
Renewed interest has emerged for primitive variable CFD formulations for the incompressible NavierStokes equations, specifically pressure relaxation schemes. Difficulties with boundary conditions and the pressure approximation space have motivated this study of a new timeaccurate formulation wherein a harmonic function replaces pressure as an algorithm variable. The resulting conservation law statement is a mixed parabolic/hyperbolic plus elliptic Poisson equation system with wellposed boundary conditions, with the incompressibility constraint naturally incorporated in the segregated formulation. A highly efficient consistent sparse factorization/Jacobi compound iteration is identified to solve the embedded Poisson equation to high accuracy thus ensuring a cost effective, timeaccurate continuity compliance. The theory and implementation of the harmonic constraint algorithm is presented and documented for a set of benchmark test problem verifications.
 Publication:

AIAA, Aerospace Sciences Meeting
 Pub Date:
 January 1990
 Bibcode:
 1990aiaa.meetY....B
 Keywords:

 Computational Fluid Dynamics;
 Incompressible Flow;
 NavierStokes Equation;
 Newtonian Fluids;
 Poisson Equation;
 Unsteady Flow;
 Algorithms;
 Boundary Conditions;
 Boundary Value Problems;
 Partial Differential Equations;
 Fluid Mechanics and Heat Transfer