A high-order stochastic Galerkin code for the compressible Euler and Navier-Stokes equations. (15th October 2021) - Dürrwächter, Jakob; Meyer, Fabian; Kuhn, Thomas; Beck, Andrea; Munz, Claus-Dieter; Rohde, Christian
Highlights: Performance-optimized stochastic Galerkin extension of a high-order code. Investigation of code performance and scaling on high performance computing systems. Application of the stochastic Galerkin code to different numerical test cases. Abstract: We present a Stochastic Galerkin (SG) scheme for Uncertainty Quantification (UQ) of the compressible Navier-Stokes and Euler equations. For spatial discretization, we rely on the high-order Discontinuous Galerkin Spectral Element Method (DGSEM) in combination with an explicit time-stepping scheme. We simulate complex flow problems in two- and three-dimensional domains using curved unstructured hexahedral meshes. The dimension of the stochastic space can be arbitrarily large. In order to treat discontinuities and to ensure hyperbolicity, we employ a multi-element approach in combination with a hyperbolicity-preserving limiter in the stochastic domain and a Finite Volume subcell shock capturing scheme in physical space. Special emphasis is put on code performance and massive parallel scalability. We demonstrate the versatility and broad applicability of our code with various numerical experiments including the supersonic flow around a spacecraft geometry. By this, we wish to contribute to the path of the Stochastic Galerkin method towards practical applicability in research and industrial engineering.