A skew-symmetric energy and entropy stable formulation of the compressible Euler equations

Abstract

We show that a specific skew-symmetric form of nonlinear hyperbolic problems leads to energy and entropy bounds. Next, we exemplify by considering the compressible Euler equations in primitive variables, transform them to skew-symmetric form and show how to obtain energy and entropy estimates. Finally we show that the skew-symmetric formulation lead to energy and entropy stable discrete approximations if the scheme is formulated on summation-by-parts form.

References in corpus (3)

• Entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations
• Nonlinear Boundary Conditions for Energy and Entropy Stable Initial Boundary Value Problems in Computational Fluid Dynamics
• Nonlinear and Linearised Primal and Dual Initial Boundary Value Problems: When are they Bounded? How are they Connected?

Cited by in corpus (6)

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• Open Boundary Conditions for Nonlinear Initial Boundary Value Problems
• A Skew-Symmetric Energy Stable Almost Dissipation Free Formulation of the Compressible Navier-Stokes Equations
• Uncertain Data in Initial Boundary Value Problems: Impact on Short and Long Time Predictions
• An Energy Stable Nonlinear Incompressible Multi-Phase Flow Formulation