The authors derive an entropy-conservative two-point flux for the ultra-relativistic Euler equations, prove its consistency, and validate an entropy-stable DG scheme against 1D radial reference solutions in 2D and 3D.
Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics
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abstract
We develop error-control based time integration algorithms for compressible fluid dynamics (CFD) applications and show that they are efficient and robust in both the accuracy-limited and stability-limited regime. Focusing on discontinuous spectral element semidiscretizations, we design new controllers for existing methods and for some new embedded Runge-Kutta pairs. We demonstrate the importance of choosing adequate controller parameters and provide a means to obtain these in practice. We compare a wide range of error-control-based methods, along with the common approach in which step size control is based on the Courant-Friedrichs-Lewy (CFL) number. The optimized methods give improved performance and naturally adopt a step size close to the maximum stable CFL number at loose tolerances, while additionally providing control of the temporal error at tighter tolerances. The numerical examples include challenging industrial CFD applications.
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Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods
The authors derive an entropy-conservative two-point flux for the ultra-relativistic Euler equations, prove its consistency, and validate an entropy-stable DG scheme against 1D radial reference solutions in 2D and 3D.