Abstract
The purpose of this paper is to demonstrate the robustness and accuracy of a provably convergent finite-volume scheme for the diffusive compressible Euler model. To this end, we consider sub- and supersonic flows as well as well-resolved smooth flows and under-resolved turbulent flows. The scheme is formulated for Voronoi meshes to allow complex geometries. It is completely defined without any parameters that require case-by-case tuning. Provable convergence guarantees both stability and admissibility of the numerical solutions, which is confirmed in our computations for both strong shocks and turbulence. For the turbulent Taylor-Green vortex, the scheme performs as well as a linearly-stable minimally-diffusive second-order scheme and for vortex shedding behind a cylinder, it even outperforms energy-stable second-order schemes.
Published Version
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