Physical Sciences and Mathematics Commons^™

Designing Adaptive Low-Dissipative High Order Schemes For Long-Time Integrations, Helen Yee, Bjorn Sjögreen

United States National Aeronautics and Space Administration: Publications

A general framework for the design of adaptive low-dissipative high order schemes is presented. It encompasses a rather complete treatment of the numerical approach based on four integrated design criteria: (1) For stability considerations, condition the governing equations before the application of the appropriate numerical scheme whenever it is possible. (2) For consistency, compatible schemes that possess stability properties, including physical and numerical boundary condition treatments, similar to those of the discrete analogue of the continuum are preferred. (3) For the minimization of numerical dissipation contamination, efficient and adaptive numerical dissipation control to further improve nonlinear stability and accuracy should …