Towards a rational theory for CFD global stability

The fundamental notion of the consistent stability of semidiscrete analogues of evolution PDEs is explored. Lyapunov's direct method is used to develop CFD semidiscrete algorithms which yield the TVD constraint as a special case. A general formula for supplying dissipation parameters for arbitrary multidimensional conservation law systems is proposed. The reliability of the method is demonstrated by the results of two numerical tests for representative Euler shocked flows.