Adaptive Multi-Grid Methods for Parallel CFD Applications

Computational fluid dynamic (CFD) computations are memory and time intensive and need to be executed in parallel for larger computational domains. In order to produce physical accurate solutions, adaptive grid setups have to be chosen as the memory and computing time would otherwise be too high, and results would not be obtained in a reasonable amount of time. This paper describes the usage of a multi-grid based approach for solving the pressure Poisson equation, arising during every time step of the Navier-Stokes equations. It will then highlight an analysis of errors introduced due to an adaptive setup of the domain, and show performance measurements for uniform and adaptive grid setups. Last but not least, a CFD benchmark example based on the von Kármán vortex street will be presented, and the results will be discussed. 48 1. Introduction. Computational fluid dynamics (CDF) simulations are time intensive and require a lot of computational resources. Hence, every optimisation or algorithmic speed-up has huge benefits for expensive long running scenarios in terms of energy efficiency and CPU costs. Moreover, design parameters regarding domain setup or solver settings also prove to have a high impact on run times. Uniform grids exhibit huge advantages due to very easy computations via stencil-based operations, they require no additional grid management, and are very easy to implement (cf. [5]). Thus, it is very cost efficient using structured uniform grids for computations. One disadvantage of such an approach is the required equidis-tant discretisation of the entire domain, which is not always necessary depending on the geometry settings. For an engineering based air-flow simulation of an indoor airspace for example, regions have to be computed very fine around obstacles but do not necessarily need to have the same resolution at regions far away from these obstacles. Thus, a geometry based, adaptively refined grid has huge advantages in terms of reducing unnecessary refinements. Adaptive grids are already quite well studied in literature. There exist several possibilities of generating adaptive grid refinements. One possibility is the stepwise approximation with regular grids, such as the approach described in this paper or from Manhart and Wengle [13]. Another possibility which will not be regarded for this code would be the overlapping of two different grids of different resolution, so called Chimera grids, as studied by Hadži´c [11]. Furthermore, boundary adapted non-orthogonal grids could be used. All methods have advantages and disadvantages listed in detail in …