High Order Accurate Space-Time Approximations for Unsteady CFD
The high order finite difference method in combination with summation-by-parts operators and weak boundary conditions can efficiently and reliably handle large problems on structured grids for reasonably smooth geometries. This has been shown in a sequence of papers in the best of journals, where the theoretical tools SBP operators, SAT boundary treatment have been described. The research code ESSENSE for flow calculations using the Navier-Stokes equations based on the SBP-SAT technique has been developed into production status in the EU FP-7 project IDIHOM (Industrialisation of Higher Order Methods). ESSENSE is currently being further developed above a collaboration project funded by VINNOVA together with SAAB and FOI. Convergence acceleration techniques such as dual time-stepping and multi-grid is added on in order to make the time-integration more efficient. The SBP-SAT described above was recently extended to the time-domain by the PI and students. It is a major breakthrough and fully discrete stable high order space-time approximations are now within reach. We further intend to extend the structured solver into the unstructured regime, by developing a hybrid version based on SBP-SAT finite difference blocks glued together with SBP-SAT spectral element blocks. These two new developments of the SBP-SAT technique require extensive testing and access to the best of computer resources available.