A Computational Approach for Multi-Body Potential-Flow Interaction Effects Using Matrix-Free FEM and Body-Conforming Grids

抄録

This paper presents a unified and computationally efficient framework for predicting incompressible, irrotational potential flow around multiple immersed bodies in two-dimensional domains, with particular emphasis on quantifying irrotational interaction effects in multi-body configurations. The methodology integrates three components: a fast body-conforming mesh generation strategy, a matrix-free finite element solution of the Laplace equation, and a systematic procedure for determining the stream function values associated with each immersed solid. Body-fitted grids are generated by imposing boundary displacements on a Cartesian background mesh followed by Laplacian smoothing, yielding simple, robust, and accurate meshes for domains containing multiple immersed bodies. The potential flow field is obtained by solving the Laplace equation using a matrix-free conjugate gradient method, wherein element-level operators are evaluated without assembling global stiffness matrices. Immersed bodies are treated as constant streamlines, and their unknown stream function values are determined through multi-point constraints that naturally capture inter-body flow connectivity. To demonstrate the capabilities of the proposed framework, potential flow interference among five cylinders arranged in both streamwise and transverse directions is examined in detail. Variations in the gap ratio δ between transverse cylinders produce changes in flow redistribution, stagnation locations, and surface velocity behaviour. The flow rate between the transverse cylinders is shown to decrease significantly at small δ because of mutual irrotational interaction with the streamwise cylinders, and this effect is quantified through the Coefficient of Potential Flow Interaction (CoPFI). The results highlight the ability of the proposed approach to resolve subtle multi-body interaction phenomena with minimal case setup effort and very low memory requirements, while providing a quantitative measure of potential flow interference in complex immersed body systems.