A Multi-resolution Fourier-Spectral and Finite-Volume Hybrid LGF Method For Solving External Flows

Lattice Green's Function (LGF), Immersed Boundary (IB) Method, and Adaptive Mesh Refinement (AMR) have been successfully combined to carry out high Reynolds number, high fidelity simulations of incompressible, external flows around bodies in a scalable and efficient manner. In this study, we extended this framework to solve fully 3D flows around nominally 2D bodies with infinite spans. Using properties of Fourier series, we developed an algorithm capable of handling multi-resolution meshes in all three spatial dimensions. Specifically, by manipulating Dirac Delta functions, we derived the evolution equations of the Fourier modes arising from Fourier expanding Navier-Stokes equations; by applying LGF of Fourier transformed Laplace operator, the algorithm solves a Poisson equation in an infinite domain with finite active grid cells; by employing the properties of truncated Fourier series, the algorithm can conduct AMR entirely in Fourier modes. Finally, we verified our algorithm using flow past cylinder at Re=300 by comparing our results to previous computations and validated the algorithm using corresponding experimental data. Currently, we are working on a flow stability algorithm based on this framework.