Abstract
•Comparison of split form and entropy stable discontinuous Galerkin methods.•Test cases of increased difficulty.•Robustness for under-resolved turbulent flows and flows with discontinuities.
In computational fluid dynamics, the demand for increasingly multidisciplinary reliable simulations, for both analysis and design optimization purposes, requires transformational advances in individual components of future solvers. At the algorithmic level, hardware compatibility and efficiency are of paramount importance in determining viability at exascale and beyond. However, equally important (if not more so) is algorithmic robustness with minimal user intervention, which becomes progressively more challenging to achieve as problem size and physics complexity increase. We numerically show that low and high order entropy stable collocated discontinuous Galerkin discretizations based on summation-by-part operators and simultaneous-approximation-terms technique provide an essential step toward a truly enabling technology in terms of reliability and robustness for both under-resolved turbulent flow simulations and flows with discontinuities.