A monolithic overset finite element method for CFD with application to bio-inspired fliers

This paper presents a monolithic finite element-based overset approach to simulate turbulent flows around moving structures using overlapping unstructured meshes. The conventional Schwarz alternating method, which iterates between overlapping subdomains by exchanging boundary conditions to obtain the solution, often suffers from slow convergence. Aiming to address this issue, we formulate a computational framework that treats overlapping subdomains as a whole system by evaluating solution continuity across subdomain boundaries as residuals in the nonlinear solving process. The approach does not necessitate iterative procedures between subdomains, leading to a practical monolithic approach. We propose two additional techniques in the framework to enable an efficient parallel implementation. Firstly, an octree-accelerated node location algorithm is developed for fast solution projection between subdomains. Secondly, since no connectivity exists for the overlapping subdomains, a parallel generalized minimal residual method (GMRES) with a composite and partial matrix-free technique is proposed to solve the linear systems covering the entire problem domain. The proposed monolithic concept is combined with arbitrary Lagrangian–Eulerian and variational multi-scale formulations (ALE-VMS) to simulate turbulent flows on moving meshes. We present the mathematical and implementation details of the proposed overset approach. Then, we verify the proposed approach using Burgers’ equation. The proposed approach is thoroughly assessed under different spatial resolutions, time step lengths, and overlapping sizes. The convergence study shows that the proposed monolithic approach outperforms the traditional Schwarz alternating method. The improved performance of the monolithic approach is further demonstrated by simulating flow past a sphere. Finally, we apply the proposed approach to simulate the aerodynamics around a bio-inspired flying system involving two fliers. The proposed approach can simultaneously maintain a boundary-fitted representation and handle the relative motion between the two fliers, delivering results that show good agreement with wind tunnel experimental data.