Numerical stability of hyperbolic equations in three independent variables

Abstract

It is shown that nonsimplicial networks proposed for the solution of hyperbolic equations in three dimensions, which satisfy the Courant-Friedrichs-Lewy condition for stability, should be further analyzed using the von Neumann condition, since the latter is a stronger necessary condition than the former for nonsimplicial networks. Several networks proposed for the solution of three-dimensional supersonic flow fields are evaluated on this basis. The stability predictions for one of the proposed networks are compared with the results of numerical experiments. This method of stability analysis also indicates an approximate degree of instability of unstable networks. With the availability of high-speed digital computers, the von Neumann condition can be tested even for complicated difference networks.