On the marching solution of elliptic equations in viscous fluid mechanics.

Marching solutions for the Poisson equation and for a set of linearized parabolized Navier-Stokes equations are considered. Enhancement of stability by high order derivatives is investigated, in order to find their influence on the accuracy and the extent of the region of integration. The results indicate that the additin of a mixed fourth order derivative damps instabilities and allows longer integration distance but may reduce the accuracy. Higher order mixed derivatives are more effective. Richardson extrapolation can be used to improve the accuracy of the stabilized solutions. (A)