Comparison of h- and p- Adaptations for Spectral Difference Methods

This paper applies some of the current mesh adaptation approaches to the high-order Spectral Difference (SD) method and investigates their performance on modeling inviscid steady flow. In particular, an entropy-based adjoint approach is used as the adaptation criterion. Both h-, p-refinement and p-coarsening are implemented. A mortar element method is used for treatment of non-conforming interfaces between grids with different sizes or orders. The performance is assessed by the accuracy of certain solution outputs (e.g. the drag coefficient) and the accuracy of capturing local flow features (e.g. shocks). While flow discontinuities are understandably better resolved with h-refinement, it is found that in regions of smooth flow, p-refinement offers a higher accuracy with the same number of degrees of freedom.