High Order Accurate Space-Time Approximations for Unsteady CFD

SNIC 2018/3-160


SNAC Medium

Principal Investigator:

Jan Nordström


Linköpings universitet

Start Date:


End Date:


Primary Classification:

10105: Computational Mathematics

Secondary Classification:

20306: Fluid Mechanics and Acoustics

Tertiary Classification:

20303: Vehicle Engineering



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 as a collaboration project together with SAAB and SMHI. 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. We also intend to investigate the forming formation of one strong vortex stemming from two aligned but separated ones. I specific interest is the formation interaction interaction itself, the new strength of the vortex and well as the sound generated. This is part of a masters thesis. These efforts above require extensive testing and access to the best of computer resources available.