COMPACT EXPLICIT FINITE-DIFFERENCE APPROXIMATIONS TO THE NAVIER-STOKES EQUATIONS.

Abstract

A review is given of some methods of obtaining explicit compact finite-difference formulae which approximate operators of the type occurring in the Navier-Stokes equations governing the motion of incompressible fluids. In their original form the coefficients which multiply the dependent variable in the formulae contain exponentials, but these can be removed by suitable expansions giving formulae with generally satisfactory computational properties. The results are developed first for operators in one space dimension and can then at once be extended to more space dimensions and time by suitable combination techniques. Approximations in which the truncation error can be either of order h**2 of h**4 in the spatial grid size h are considered.