Error-estimate based adaptive mesh refinement

Abstract

Computational fluid dynamics (CFD) has become an indispensable tool in research and engineering. Even though the performance of computers is increasing at unfathomable speeds, the calculation of many fluid problems remains to be challenging. With the emerging widespread use of Large Eddy Simulation (LES), the computational cost of simulations has further increased. Nowadays, the successful application of CFD is highly dependent on the user. A crucial factor that influences computational performance, as well as the accuracy and reliability of the simulation results, is the underlying spatial discretization of CFD problems. Adaptive mesh refinement has the potential to address these issues, by automatically creating a computationally-efficient and user-independent mesh. The objective of this Master's thesis is to improve the computational efficiency of LES CFD simulations by developing and testing a novel more user-independent AMR error sensor. A series of novel error sensors are proposed that are based on an error estimate, which is obtained during run-time by comparing the results of a fine and coarse-grained simulation. A popular reference error sensor based on the curvature of velocity magnitude is used as a comparison in three different test cases: Mach 3 flow over a forward-facing step, flow over a two-dimensional cylinder at Re=100, and flow over periodic hills at Re=10595. All error sensors performed similarly for the Mach 3 flow over a forward-facing step. Essential flow features such as the bow shock, shock reflections, and slip lines were captured and well resolved. Differences in performance were mainly attributed to the control of the adaption routine. Anisotropic refinement led to a further error reduction in the range of 10 to 15%. Performance in the laminar two-dimensional cylinder case varied substantially. The novel error sensor based on the percentage error in the solution performed the best, leading to up to five times the computational savings in comparison to the reference indicator. Across all tests, anisotropic refinement was not able to lead to any computational savings when considering the run-time of the problem. The performance of all error sensors was underwhelming for the flow over periodic hills. The error sensors failed to refine the upper wall, which, without wall-function, lead to a significant error in the solution. The overall performance of some novel error sensors was shown to be promising. Large computational savings in a robust user-independent AMR routine were presented for the compressible and laminar cases. However, more research is required for the successful applications in turbulent flows. Arguments were presented that highlight why adaption based on a target mesh size in conjunction with mesh coarsening is superior to regular threshold-based adaption. Directions and possible solutions to make adaption for turbulent flows successful are given as well.