AN EXTENDED LAGRANGIAN METHOD

A unique formulation of describing fluid motion is presented. The meth od, referred to as ''extended Lagrangian method,'' is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion result ing from mixing of fluxes in the Eulerian description. The present met hod and the Arbitrary Lagrangian-Eulerian (ALE) method have a similari ty in spirit-eliminating the cross-streamline numerical diffusion. For this purpose, we suggest a simple grid constraint condition and utili ze an accurate discretization procedure. This grid constraint is only applied to the transverse cell face parallel to the local stream veloc ity, and hence our method for the steady state problems naturally redu ces to the streamline-curvature method, without explicitly solving the steady streamline-coordinate equations formulated a priori. Unlike th e Lagrangian method proposed by Loh and Hui which is valid only for st eady supersonic flows, the present method is general and capable of tr eating subsonic flows and supersonic flows as well as unsteady flows, simply by invoking in the same code an appropriate grid constraint sug gested in this paper. The approach is found to be robust and stable. I t automatically adapts to flow features without resorting to clusterin g, thereby maintaining rather uniform grid spacing throughout and larg e time step. Moreover, the method is shown to resolve multi-dimensiona l discontinuities with a high level of accuracy, similar to that found in one-dimensional problems. (c) 1995 Academic Press. Inc.