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

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.

arXiv comment39 pages. arXiv admin note: substantial text overlap with arXiv:1911.03682 and text overlap with arXiv:1905.03007 by other authors

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Cited by in corpus (11)

• Fully-Discrete Explicit Locally Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations
• Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes
• Entropy Stable Discontinuous Galerkin Methods for Balance Laws in Non-Conservative Form: Applications to the Euler Equations with Gravity
• Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws
• On error-based step size control for discontinuous Galerkin methods for compressible fluid dynamics
• Entropy-Stable Gauss Collocation Methods for Ideal Magneto-Hydrodynamics
• On the robustness of high-order upwind summation-by-parts methods for nonlinear conservation laws
• Generalized upwind summation-by-parts operators and their application to nodal discontinuous Galerkin methods
• On a linear stability issue of split form schemes for compressible flows
• Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics
• Efficient computation of Jacobian matrices for entropy stable summation-by-parts schemes