Browsing by Author "Munz, Claus-Dieter"

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Open Access
Discontinuous Galerkin methods for the unsteady compressible Navier-Stokes equations
(2009) Gassner, Gregor; Munz, Claus-Dieter
In this work a new explicit arbitrary high order accurate discontinuous Galerkin finite element solver for the unsteady compressible Navier-Stokes equations is developed. Although the focus is on the compressible Navier-Stokes equations, the developed framework can directly be applied to other pure hyperbolic, pure parabolic or mixed hyperbolic/parabolic time dependent conservation laws. Discontinuous Galerkin finite element based methods have several important properties. They are locally conservative schemes, despite their affiliation to the class of finite element methods. They allow to use arbitrary unstructured non-conforming meshes, while remaining their formal (high) order of accuracy, even with skewed and anisotropic grid cells. The resolution can be adapted locally by increasing or decreasing the local polynomial degree, without the difficulties of a conforming finite element approach. The (formal) order of accuracy is essential a parameter, as one only has to choose the polynomial degree of the approximation. The most important property of discontinuous Galerkin schemes is that the solution in a grid cell depends only on data from grid cells sharing a face, independent of the approximation order. This compactness yields an excellent parallelizability of the method, which is essential for large scale computations. Based on the standard spatial discontinuous Galerkin framework several modifications to increase the computational efficiency are proposed. In a first step a novel construction guideline for modal and nodal basis functions on arbitrary shaped grid cells is introduced. For the discretization of problems with high order derivatives a novel weak formulation is introduced and applied to the second order compressible Navier-Stokes equations. For the approximation of the viscous fluxes a new approximation based on local Riemann solutions is used. This spatial discretization is combined with a new time discretization, which allows time consistent local time stepping. In order to validate the high accuracy and efficiency of the developed method, several test cases including the linearized Euler equations, the non-linear Euler equations and the compressible Navier-Stokes equations are considered. Finally, this method is applied to solve two and three dimensional compressible unsteady flow problems.
Open Access
An efficient hp-adaptive strategy for a level-set ghost-fluid method
(2023) Mossier, Pascal; Appel, Daniel; Beck, Andrea D.; Munz, Claus-Dieter
We present an hp-adaptive discretization for a sharp interface model with a level-set ghost-fluid method to simulate compressible multiphase flows. The scheme applies an efficient p-adaptive discontinuous Galerkin (DG) operator in regions of smooth flow. Shocks and the phase interface are captured by a Finite Volume (FV) scheme on a h-refined element-local sub-grid. The resulting hp-adaptive scheme thus combines both the high order accuracy of the DG method and the robustness of the FV scheme by using p-adaptation in smooth areas and h-refinement at discontinuities, respectively. For the level-set based interface tracking, a similar hybrid DG/FV operator is employed. Both p-refinement and FV shock and interface capturing are performed at runtime and controlled by an indicator, which is based on the modal decay of the solution polynomials. In parallel simulations, the hp-adaptive discretization together with the costly interface tracking algorithm cause a significant imbalance in the processor workloads. To ensure parallel efficiency, we propose a dynamic load balancing scheme that determines the workload distribution by element-local wall time measurements and redistributes elements along a space filling curve. The parallelization strategy is supported by strong scaling tests using up to 8192 cores. The framework is applied to established benchmarks problems for inviscid, compressible multiphase flows. The results demonstrate that the hybrid adaptive discretization can efficiently and accurately handle complex multiphase flow problems involving pronounced interface deformations and merging interface contours.
Open Access
A p-adaptive discontinuous Galerkin method with hp-shock capturing
(2022) Mossier, Pascal; Beck, Andrea; Munz, Claus-Dieter
In this work, we present a novel hybrid Discontinuous Galerkin scheme with hp-adaptivity capabilities for the compressible Euler equations. In smooth regions, an efficient and accurate discretization is achieved via local p-adaptation. At strong discontinuities and shocks, a finite volume scheme on an h-refined element-local subgrid gives robustness. Thus, we obtain a hp-adaptive scheme that exploits both the high convergence rate and efficiency of a p-adaptive high order scheme as well as the stable and accurate shock capturing abilities of a low order finite volume scheme, but avoids the inherent resolution loss through h-refinement. A single a priori indicator, based on the modal decay of the local polynomial solution representation, is used to distinguish between discontinuous and smooth regions and control the p-refinement. Our method is implemented as an extension to the open source software FLEXI. Hence, the efficient implementation of the method for high performance computers was an important criterion during the development. The efficiency of our adaptive scheme is demonstrated for a variety of test cases, where results are compared against non adaptive simulations. Our findings suggest that the proposed adaptive method produces comparable or even better results with significantly less computational costs.