Adaptation of the hybrid fictitious domain-immersed boundary method for Reynolds-averaged turbulence modeling
For engineers performing shape or topology optimization, this method removes the remeshing bottleneck while maintaining accuracy, though it is an incremental adaptation of existing methods.
The paper adapts a hybrid fictitious domain-immersed boundary method for RANS turbulence modeling to avoid frequent remeshing in CFD-based topology optimization. The framework achieves results consistent with body-fitted CFD for Reynolds numbers from 10^1 to 10^6 across several benchmarks.
Engineering practice often calls for shape or topology optimization (TO) of fluid defining components, while the ever-increasing computing power allows the optimized cost functions to be based on computational fluid dynamics (CFD). However, a common bottleneck in CFD-based TO frameworks is the requirement for frequent remeshing. In order to alleviate this bottleneck, we propose an adaptation of an immersed boundary (IB) method variant, the hybrid fictitious domain-immersed boundary method, to leverage Reynolds-averaged Navier-Stokes (RANS) equations and wall function. The main contribution of the present work lies in the design and open-source implementation of the IB-aware steady-state solution of the RANS equations via the SIMPLE algorithm in the OpenFOAM library. For the most common two-equation RANS models, Reynolds numbers from $10^1$ to $10^6$, and several benchmarks, such as flow over a backwards facing step or an Ahmed body, the framework gives results consistent with the standard body-fitted CFD. Furthermore, given the intended application in TO, special emphasis is placed on the robustness and applicability of the approach to general geometries, which is tested on a NACA profile under various angles of attack.