Development of a Scalable Method for the Efficient Simulation of Flows using Dynamic Goal-Oriented Local Grid-Adaptation

Abstract Flows in marine applications are characterized by very high Reynolds numbers and complex three-dimensional geometries, which in combination often lead to localized turbulent structures. Furthermore, most flows include free surfaces. For both features, localized turbulent structures and free surfaces, a sufficiently fine local grid resolution is indispensable to achieve accurate solutions. On the other hand the effort for solving flow problems increases with increasing numbers of cells and the locations for the local grid refinement depends on the solution of the flow. Therefore, it is hardly possible to generate optimal grids, meaning using a minimum number of cells to solve a problem accurately, before knowing the solution for the flow problem. A well known technique to overcome this problem is dynamic local grid-adaptation, where the grid is adapted to the flow during the solution process. Although being a well known technique, the number of applications that are feasible to perform local grid-adaptation in turbulent flows for complex threedimensional geometries is limited, which is caused by the high complexity of the software implementation and the lack of appropriate grid refinement indicators. Within this work the algorithm to perform local anisotropic grid-adaptation for hexahedral cells in a parallel unstructured grid environment is described in detail. The developed grid-adaptation technique is combined with different grid refinement indicators, ranging from simple feature based indicators via error estimators to sophisticated goal-oriented indicators for threedimensional turbulent flows. Simple feature based indicators refine the grid at specific flow features without any link to an error or a stopping criterion for the refinement. Error estimator based refinement indicators try to estimate the error for each cell in the domain and to minimise the error by refining the grid at locations associated with large errors. However, they do not provide a link between the local errors and their influence on a scalar quantity of interest (e.g. drag). Goal-oriented error estimators link the local errors to the error in a scalar (global) quantity of interest and hence indicate refinement only in those cells where the local error has an influence on the global quantity of interest. Furthermore, it is possible to define a desired range of accuracy for the global quantity of interest to provide a stopping criterion for the refinement. In addition to the developed grid refinement technique, methods to enhance the accuracy of the VoF method, widely used for free-surface flows within finite volume flow solvers, are developed. The accuracy of the method is enhanced by the application of an Explicit Interface Sharpening (EIS) technique, which is able to resharpen blurred surfaces. The efficiency is enhanced by means of a sub-cycling technique, solving the transport equation for the mixture fraction with smaller time steps than the other transport equations. For the sub-cycling technique two dedicated modes associated to flow problems which lead to steady and transient solutions are developed.