Entropy Stable h/p-Nonconforming Discretization with the Summation-by-Parts Property for the Compressible Euler and Navier-Stokes Equations
| Autor: | Fernandez, David C. Del Rey, Carpenter, Mark H., Dalcin, Lisandro, Zampini, Stefano, Parsani, Matteo |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this paper, the entropy conservative/stable algorithms presented by Del Rey Fernandez and coauthors [18,16,17] for the compressible Euler and Navier-Stokes equations on nonconforming p-refined/coarsened curvilinear grids is extended to h/p refinement/coarsening. The main difficulty in developing nonconforming algorithms is the construction of appropriate coupling procedures across nonconforming interfaces. Here, a computationally simple and efficient approach based upon using decoupled interpolation operators is utilized. The resulting scheme is entropy conservative/stable and element-wise conservative. Numerical simulations of the isentropic vortex and viscous shock propagation confirm the entropy conservation/stability and accuracy properties of the method (achieving ~ p + 1 convergence) which are comparable to those of the original conforming scheme [4,35]. Simulations of the Taylor-Green vortex at Re = 1,600 and turbulent flow past a sphere at Re = 2,000 show the robustness and stability properties of the overall spatial discretization for unstructured grids. Finally, to demonstrate the entropy conservation property of a fully-discrete explicit entropy stable algorithm with h/p refinement/coarsening, we present the time evolution of the entropy function obtained by simulating the propagation of the isentropic vortex using a relaxation Runge-Kutta scheme. Comment: 37 pages. arXiv admin note: text overlap with arXiv:1909.12536, arXiv:1909.12546 |
| Databáze: | arXiv |
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