Adaptive mesh refinement in complex flow simulations

Adaptive mesh refinement (AMR) involves dynamically adjusting the computational grid resolution during a numerical simulation based on the local properties of the solution, allowing the simulations to concentrate computational resources in regions of high complexity or rapid changes. As a result, AMR has made turbulent flow simulations at very high Reynolds numbers more practical. However, AMR strategy may also adversely affect the solution accuracy if not done carefully. For instance, AMR strategy generally requires a user-defined cut-off value on a flow parameter like vorticity, based on a priori knowledge of the flow, to select all the appropriate grid zones for further refinement. Sometimes, this strategy may also ignore regions with important flow physics, e.g., high strain-rate regions. To avoid these issues, we propose an AMR strategy where the grid zones are selected for refinement by optimizing a sub-modular set function. This function is representative of the captured complexity in flow physics or numerical accuracy of the simulation and does not require a priori knowledge of the flow. This optimization strategy is implemented in Python and integrated with a c++ based CFD toolbox, OpenFOAM. The initial simulations of canonical flows with this strategy have shown promising results, and further details of the approach with simulations of complex flows will be presented at the meeting.