SC²S Colloquium - February 24, 2017

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Date: February 24, 2017
Room: 02.07.023
Time: 3:00 pm, s.t.

Saumitra Vinay Joshi: Adaptive Mesh Refinement in OpenFOAM with Quantified Error Bounds and Support for Arbitrary Cell-types

Adaptive Mesh Refinement (AMR) plays a pivotal role in the balance of computational cost and solution accuracy. The version of AMR shipped with the latest OpenFOAM release is capable of refining and coarsening hexahedral cells based on a solution variable and a refinement range, both of which need to be specified by the user. Adaptivity in this sense is rather naive and lacks generalized accuracy estimates derived from sound mathematical reasoning. The focus of this thesis was to develop an upgraded AMR algorithm that ensures the following two properties: Guaranteed error bounds: The upgraded algorithm uses a refinement criterion based on the concept of multiresolution analysis to ensure the boundedness of mesh coarsening error to that of the underlying solution scheme. Furthermore, the criterion is fully automatic, leading to user independence from having to provide a value range. Support for arbitrary cell types: A robust subdivision algorithm for cells of arbitrary shapes is developed and implemented. This involves the decomposition of polyhedral cells into tetrahedra, followed by their recursive refinement and coarsening. The revamped AMR algorithm promises accuracy to the order of a full grid of equivalent refinement. It leads to improved performance in terms of speed, CPU memory requirements, and storage. With support for arbitrary cell shapes, the AMR algorithm is applicable to a wider range of cases. The impact of the thesis on these features is analysed through a suite of benchmark simulations.