Accurate and Stable Calculations Involving Shocks Using a Hybrid Scheme

Qaisar Abbas
Division of Scientific Computing
Department of Information Technology
Uppsala University

Abstract:

We develop a hybrid scheme consisting of a combination of a second order MUSCL scheme and a high order finite difference scheme. The full hybrid scheme is constructed in such a way that we can prove that it is stable for linear problems. We show by numerical experiments that it is high order accurate in smooth domains and oscillatory free close to shocks.