A stable and conservative method for locally adapting the design order of finite difference schemes
A procedure to locally change the order of accuracy of finite difference schemes is developed. The development is based on existing Summation-By-Parts operators and a weak interface treatment. The resulting scheme is proven to be accurate and stable. Numerical experiments verify the theoretical accuracy for smooth solutions. In addition, shock calculations are performed, using a scheme where the developed switching procedure is combined with the MUSCL technique.
conservation summation-by-parts shock calculations finite difference methods high order accuracy stability