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

TL;DR

This paper introduces a fast, matrix-free finite element framework with body-conforming grids for accurately predicting potential flow interactions among multiple immersed bodies, emphasizing efficiency and minimal setup.

Contribution

It develops a unified, computationally efficient method combining mesh generation, matrix-free FEM, and systematic stream-function determination for multi-body potential flow analysis.

Findings

Accurately captures subtle multi-body interaction effects.

Uses minimal memory and setup effort.

Provides quantitative flow interference measures.

Abstract

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-\,$\psi$ streamlines, and their unknown stream-function values are determined through multi-point constraints that naturally capture inter-body flow connectivity. 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.