On the robustness and performance of entropy stable discontinuous collocation methods for the compressible Navier-Stokes equations

TL;DR

This paper demonstrates that entropy stable discontinuous collocation methods significantly enhance the robustness and reliability of simulations for complex compressible Navier-Stokes flows, especially under challenging conditions like turbulence and discontinuities.

Contribution

It introduces entropy stable discontinuous collocation methods based on summation-by-part operators that improve robustness and reliability in fluid dynamics simulations.

Findings

Enhanced robustness in turbulent flow simulations.

Effective handling of flow discontinuities.

Potential for reliable exascale computing applications.

Abstract

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 discontinuous spatial discretizations based on summation-by-part operators and simultaneous-approximation-terms technique provides 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.