A multiscale framework for multiphase flow based on the compressible Navier-Stokes-Korteweg system

Abstract

Turbulent inflow methods offer new possibilities for an efficient simulation by reducing the computational domain to the interesting parts. Typical examples are turbulent flow over cavities, around obstacles or in the context of zonal large eddy simulations. Within this work, we present the current state of two turbulent inflow methods implemented in our high order discontinuous Galerkin code FLEXI with special focus laid on HPC applications. We present the recycling-rescaling anisotropic linear forcing (RRALF), a combination of a modified recycling-rescaling approach and an anisotropic linear forcing, and a synthetic eddy method (SEM). For both methods, the simulation of a turbulent boundary layer along a flat plate is used as validation case. For the RRALF method, a zonal large eddy simulation of the rear part of a tripped subsonic turbulent boundary layer over a flat plate is presented. The SEM is validated in the case of a supersonic turbulent boundary layer using data from literature at the inflow. In the course of the cluster upgrade to the HPE Apollo system at HLRS, our framework was examined for performance on the new hardware architecture. Optimizations and adaptations were carried out, for which we will present current performance data.

Abstract

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.

Abstract

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.

Abstract

This paper summarizes our progress in the application and improvement of a high order discontinuous Galerkin (DG) method for scale resolving fluid dynamics simulations towards robust and flexible industrial applications. We report the results obtained on the Cray XC40 Hazel Hen cluster at HLRS and show code performance. We present three application cases and developments: An implicit time integration scheme for split-form DG schemes allows us to solve stiff problems with increased efficiency, which will open up new classes of problems for simulations with FLEXI. We follow this by discussing a Large Eddy Simulation (LES) of a compressible turbulent boundary layer and provide comparison to DNS data. Lastly, we demonstrate how to extend the high order scheme with a consistent and conservative sliding mesh interface, and present results of a 1.5 stage turbine simulation with wall-resolved LES.