Adaptation of the hybrid fictitious domain-immersed boundary method for Reynolds-averaged turbulence modeling

2026-06-04

AI Summary

This study addresses the computational bottleneck caused by frequent remeshing in CFD-based fluid topology optimization by proposing a steady-state solver framework that integrates the fictitious domain method with the immersed boundary (IB) approach. For the first time, an open-source IB solver supporting two-equation RANS models and wall functions is implemented in OpenFOAM. Built upon the SIMPLE algorithm for solving Reynolds-averaged Navier–Stokes equations, the method eliminates the need for body-fitted meshes, significantly enhancing geometric flexibility and optimization robustness. Validation across benchmark cases—including backward-facing step flows, the Ahmed body, and NACA airfoils at multiple angles of attack—demonstrates excellent agreement with conventional body-fitted CFD results over a Reynolds number range of 10¹ to 10⁶, confirming the solver’s accuracy and broad applicability.

Abstract

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.

Problem

• topology optimization
• computational fluid dynamics
• remeshing
• Reynolds-averaged Navier-Stokes
• immersed boundary method

Innovation

• immersed boundary method
• RANS modeling
• topology optimization
• OpenFOAM
• mesh-free CFD