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This work presents GALAEXI as a novel, energy-efficient flow solver for the simulation of compressible flows on unstructured meshes leveraging the parallel computing power of modern Graphics Processing Units (GPUs). GALAEXI implements the high-order Discontinuous Galerkin Spectral Element Method (DGSEM) using shock capturing with a finite-volume subcell approach to ensure the stability of the high-order scheme near shocks. This work provides details on the general code design, the parallelization strategy, and the implementation approach for the compute kernels with a focus on the element local mappings between volume and surface data due to the unstructured mesh. GALAEXI exhibits excellent strong scaling properties up to 1024 GPUs if each GPU is assigned a minimum of one million degrees of freedom degrees of freedom. To verify its implementation, a convergence study is performed that recovers the theoretical order of convergence of the implemented numerical schemes. Moreover, the solver is validated using both the incompressible and compressible formulation of the Taylor-Green-Vortex at a Mach number of 0.1 and 1.25, respectively. A mesh convergence study shows that the results converge to the high-fidelity reference solution and that the results match the original CPU implementation. Finally, GALAEXI is applied to a large-scale wall-resolved large eddy simulation of a linear cascade of the NASA Rotor 37. Here, the supersonic region and shocks at the leading edge are captured accurately and robustly by the implemented shock-capturing approach. It is demonstrated that GALAEXI requires less than half of the energy to carry out this simulation in comparison to the reference CPU implementation. This renders GALAEXI as a potent tool for accurate and efficient simulations of compressible flows in the realm of exascale computing and the associated new HPC architectures., Comment: 19 pages, 12 figures, 3 tables. Accepted Manuscript. Code available at: https://github.com/flexi-framework/galaexi

Modern high-order discretizations bear considerable potential for the exascale era due to their high fidelity and the high, local computational load that allows for computational efficiency in massively parallel simulations. To this end, the discontinuous Galerkin (DG) framework FLEXI was selected to demonstrate exascale readiness within the Center of Excellence for Exascale CFD (CEEC) by simulating shock buffet on a three-dimensional wing segment at transsonic flight conditions. This paper summarizes the recent progress made to enable the simulation of this challenging exascale problem. For this, it is first demonstrated that FLEXI scales excellently to over 500 000 CPU cores on HAWK at the HLRS. To tackle the considerable resolution requirements near the wall, a novel wall model is proposed that takes compressibility effects into account and yields decent results for the simulation of a NACA 64A-110 airfoil. To address the shocks in the domain, a finite-volume-based shock capturing method was implemented in FLEXI, which is validated here using the simulation of a linear compressor cascade at supersonic flow conditions, where the method is demonstrated to yield efficient, robust and accurate results. Lastly, we present the TensorFlow-Fortran-Binding (TFFB) as an easy-to-use library to deploy trained machine learning models in Fortran solvers such as FLEXI., Comment: 15 pages, 5 figures

Sliding meshes are a powerful method to treat deformed domains in computational fluid dynamics, where different parts of the domain are in relative motion. In this paper, we present an efficient implementation of a sliding mesh method into a discontinuous Galerkin compressible Navier-Stokes solver and its application to a large eddy simulation of a 1-1/2 stage turbine. The method is based on the mortar method and is high-order accurate. It can handle three-dimensional sliding mesh interfaces with various interface shapes. For plane interfaces, which are the most common case, conservativity and free-stream preservation are ensured. We put an emphasis on efficient parallel implementation. Our implementation generates little computational and storage overhead. Inter-node communication via MPI in a dynamically changing mesh topology is reduced to a bare minimum by ensuring a priori information about communication partners and data sorting. We provide performance and scaling results showing the capability of the implementation strategy. Apart from analytical validation computations and convergence results, we present a wall-resolved implicit LES of the 1-1/2 stage Aachen turbine test case as a large scale practical application example.