Algorithm For Solution Of Navier-Stokes Equations

Abstract

Advantages of two previous algorithms combined. Steady-state Navier-Stokes equations put in implicit finite-difference form solved by approximate Newton iteration. LU-SSOR scheme is new relaxation method combining advantages of LU factorization with Gauss-Seidel relaxation. Vectorizable LU-SSOR scheme, based on central differences, requires scalar diagonal inversions. Application of scheme to approximate Newton iteration of Navier-Stokes equations yields set of equations requiring no implicit smoothing on left side. Only adaptive, total-variation-diminishing, flux-limited dissipation terms added to right side. Algorithm used to predict laminar, turbulent, and hypersonic flows.