A systematic analysis of three-dimensional Riemann problems for verification of compressible-flow solvers

Numerical simulation is a well-established way of analyzing compressible flows. Due to high computational demands of solvers for such flow problems, their verification is typically limited to two-dimensional (2D) cases. However, 2D simulations suppress fundamental three-dimensional (3D) aspects of the flow evolution in (compressible) turbulent flows or shock-bubble and shock-drop interactions. With increase of computational power, 3D simulations become more feasible for routine analyses. The verification of 3D simulation frameworks is often limited to transformations of lower dimensional test cases in the 3D space. There is a lack of strictly 3D reference test cases for gas dynamics. In this work, we present a set of genuine 3D Riemann problems in order to validate and verify numerical solvers for compressible flows. The problems are designed such that each octant's constant initial data connects two neighboring states by an elementary wave only. The problem design is inspired by well-established 2D Riemann problems most prominently posted by Lax and Liu (1998). In contrast to the twenty published 2D cases, more than 300 distinct combinations can be found in 3D. We provide example solutions for the particularly interesting ones of these case combinations and show how the cases help to expose shortcomings of numerical solvers. We provide reference data from computations with an open-source compressible multiresolution flow solver. For the reference solutions, we employ the Harten-Lax-van Leer contact (HLLC) Riemann solver and a weighted essentially non-oscillatory (WENO) reconstruction stencil of fifth order. The reference solutions use an effective resolution of one billion cells. We additionally make the full compute pipeline of this work publicly available, so interested researchers may reproduce and extend the current work. © 2024 The Author(s)     «

Numerical simulation is a well-established way of analyzing compressible flows. Due to high computational demands of solvers for such flow problems, their verification is typically limited to two-dimensional (2D) cases. However, 2D simulations suppress fundamental three-dimensional (3D) aspects of the flow evolution in (compressible) turbulent flows or shock-bubble and shock-drop interactions. With increase of computational power, 3D simulations become more feasible for routine analyses. The ver...     »

Funding text 1 The authors would like to thank Dr. Steffen Schmidt for fruitful discussion on multidimensional Riemann problems. The authors have received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 667483). The first author would like to thank the Federal Government and the Heads of Government of the L\u00E4nder, as well as the Joint Science Conference (GWK), for their funding and support within the framework of the NFDI4Ing consortium. Funded by the German Research Foundation (DFG) - project number 442146713. The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. for funding this project by providing computing time on the CoolMUC-2 Linux-Cluster at Leibniz Supercomputing Centre. Funding text 2 The authors have received funding from the European Research Council (ERC) under the European Union\u2019s Horizon 2020 research and innovation programme (grant agreement No. 667483 ). Funding text 3 The first author would like to thank the Federal Government and the Heads of Government of the L\u00E4nder, as well as the Joint Science Conference (GWK), for their funding and support within the framework of the NFDI4Ing consortium. Funded by the German Research Foundation (DFG) - project number 442146713 .      «

Funding text 1 The authors would like to thank Dr. Steffen Schmidt for fruitful discussion on multidimensional Riemann problems. The authors have received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 667483). The first author would like to thank the Federal Government and the Heads of Government of the L\u00E4nder, as well as the Joint Science Conference (GWK), for their funding and support within...     »