A Cut Cell Discontinuous Galerkin Method for Particulate Flows

Today, there are still numerous phenomena of particulate flows in engineering and nature which are not fully understood. This results out of a lack of accurate and computationally efficient solvers in this field, especially when it comes to particles which deform to various shapes. The discontinuous Galerkin method can provide both, high accuracy and efficient parallelization due to its high order convergence and cell local formulations. Thus, it is a promising approach to better understand the underlying physics. In this work a cut cell discontinuous Galerkin method is developed for particles with non-spherical shape. It is based on an immersed boundary approach to avoid costly remeshing. For the fluid part the Navier-Stokes equations and for the particle motion the Newton-Euler equations are solved. To connect both, a two-way coupling strategy is applied. It consists of the calculation of hydrodynamic forces acting on the particle and implying Dirichlet velocity boundary conditions on the particle surface for the fluid part. Furthermore, two collision models are implemented, both using a detection algorithm based on cut cells which also works for boundaries with arbitrary shape. Various numerical experiments with increasing complexity show the high accuracy of the method by comparing the obtained results with literature. The investigations start from simple immersed boundary cases with non-moving domains to fully-coupled simulations of multiple particles falling in incompressible fluid. The method is extended to three dimensional problems to investigate a sphere at a Reynolds number of 700 as a proof of the possibility applying the proposed method to larger problems. In order to obtain results for the three dimensional test in a reasonable time, the convergence of a newly implemented Newton-Krylov method with different preconditioning techniques is investigated. Further, the proposed method is optimized to run on multiple cores in parallel. For this, a performance analysis workflow for the open source framework BoSSS on high-performance computing (HPC) systems is presented. With this, a single-core performance analysis and tests focusing on the parallel efficiency of the current code are performed. In the end, the proposed method shows both, the ability of computing high accurate solutions for particulate flows and a good parallel scaling behavior on modern HPC systems