NONCONSERVATIVE HYBRID SHOCK CAPTURING SCHEMES

We examine some efficient numerical approximations for hyperbolic systems of conservation laws. The approximations are constructed by hybridizing simple, accurate centered difference schemes (for use in smooth regions), with sophisticated shock capturing schemes (for use only in narrow zones near shocks and other singularities). The switching strategies we consider are very flexible in allowing one to choose schemes independently for different regions of the flow. The resulting hybrid schemes need not be conservative. But numerical examples in one dimension demonstrate that if the switching strategy is cautious (e.g., if switching is prohibited too close to shocks), then high accuracy can be achieved for both shock speeds and smooth regions. For one switching strategy in particular it is easy to prove convergence to the entropy solution. © 1993 Academic Press, Inc.