Keywords

vortex particle method, panel method, VPM, Krylov, fast multipole method, FMM, matrix-free, multigrid, boundary element, gauss-seidel, linear solve

Abstract

Design of vertical takeoff and landing aircraft is challenging in part due to significant aerodynamic interactions between rotors and wings. Computational models can aid in their design, but are computationally expensive. 3-D panel methods coupled with vortex particle wakes offer an attractive solution, but solving for the panel strengths scales poorly for large problems. Multigrid methods, such as Krylov subspace methods in conjunction with the fast multipole method (FMM), have been demonstrated to reduce the scaling to O(𝑁). We explore the performance and limitations of the Krylov-FMM method, traditional matrix-powered GMRES, LU decomposition, and a novel O(𝑁) multigrid approach to solving boundary element problems by combining FMM with Gauss-Seidel iterations. We also explore the effect of warm-starting these methods in unsteady aerodynamic simulation, leading to an order-of-magnitude decrease in cost.

Original Publication Citation

Anderson, R., and Ning, A., “Solving Unsteady Potential Flow Problems in O(n) Time,” AIAA Aviation Forum, Las Vegas, Jul. 2024. doi:10.2514/6.2024-4018