DISCRETE COMPATIBILITY IN FINITE-DIFFERENCE METHODS FOR VISCOUS INCOMPRESSIBLE FLUID-FLOW

Thom's vorticity condition for solving the incompressible Navier-Stoke s equations is generally known as a first-order method since the local truncation error for the value of boundary vorticity is first-order a ccurate. In the present paper, it is shown that convergence in the bou ndary vorticity is actually second order for steady problems and for t ime-dependent problems when t > 0. The result is proved by looking car efully at error expansions for the discretization which have been prev iously used to show second-order convergence of interior vorticity. Nu merical convergence studies confirm the results. At t = 0 the computed boundary vorticity is first-order accurate as predicted by the local truncation error. Using simple model problems for insight we predict t hat the size of the second-order error term in the boundary condition blows up like C/root t as t --> 0. This is confirmed by careful numeri cal experiments. A similar phenomenon is observed for boundary vortici ty computed using a primitive method based on the staggered marker-and -cell grid. (C) 1996 Academic Press, Inc.