SC²S Colloquium - July 20, 2016

Date:	July 20, 2016
Room:	02.07.023
Time:	3:00 pm, s.t.

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

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 my work would be two-fold: 1. Guaranteed error bounds: This task would involve alteration of the nature of adaptivity such that it ensures the boundedness of mesh coarsening error to that of the underlying solution scheme. Multiresolution analysis emerges as an ideal foundation for this purpose. An added benefit of this feature would be a fully automatic governing criterion for refinement, leading to user independence from having to provide a value range. 2. Support for arbitrary cell types: The objective of this task would be the development and implementation of a robust subdivision algorithm for cells of arbitrary shapes. Retaining cell quality is a major hurdle that would need to be overcome in this process. This would be followed by extension of accuracy-oriented adaptivity to these cells. The revamped AMR algorithm promises accuracy to the order of a full grid of equivalent refinement. It would lead to improved performance, at least in terms of CPU memory requirements. With support for arbitrary cell shapes, the AMR algorithm would be applicable to a wider range of cases. The impact of the thesis on these features will be analysed through a suite of benchmark simulations