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

Anil Lal S, Mannu Yadav

TL;DR

The paper addresses rapid prediction of potential flow around multiple immersed bodies in 2D by integrating a fast body‑conforming mesh, a matrix‑free FEM solver for the Laplace equations, and a systematic multi‑point constraint approach to assign constant body stream‑function values. The method yields accurate flow nets and surface tangential velocities with low memory usage, validated against analytic results and demonstrated on a five‑cylinder configuration to quantify inter‑body irrotational interference via CoPFI. A cubic polynomial fit for CoPFI(δ) enables predictive interpolation of interference effects across gap ratios δ. The framework supports rapid design optimization and parametric studies in aerospace, marine, and industrial contexts, with potential extensions to incorporate viscous corrections and coupling to more detailed models.

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-\,$ψ$ 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.

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

TL;DR

The paper addresses rapid prediction of potential flow around multiple immersed bodies in 2D by integrating a fast body‑conforming mesh, a matrix‑free FEM solver for the Laplace equations, and a systematic multi‑point constraint approach to assign constant body stream‑function values. The method yields accurate flow nets and surface tangential velocities with low memory usage, validated against analytic results and demonstrated on a five‑cylinder configuration to quantify inter‑body irrotational interference via CoPFI. A cubic polynomial fit for CoPFI(δ) enables predictive interpolation of interference effects across gap ratios δ. The framework supports rapid design optimization and parametric studies in aerospace, marine, and industrial contexts, with potential extensions to incorporate viscous corrections and coupling to more detailed models.

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-\, 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.

Paper Structure

This paper contains 10 sections, 16 equations, 10 figures, 1 table, 1 algorithm.

Table of Contents

  1. Practical Applications
  2. Introduction
  3. Body-Conforming Grid Generation
  4. Matrix-Free Potential-Flow Solver
  5. Validation
  6. Results and Discussion
  7. Conclusions
  8. Data Availability Statement
  9. Appendixes
  10. Algorithm

Figures (10)

  • Figure 1: Schematic diagram of the mixed-cells mesh formation over an immersed body.
  • Figure 2: The final mesh developed in a rectangular domain containing one immersed cylinder
  • Figure 3: Surface velocity distribution over a cylinder and comparison with the analytical solution
  • Figure 4: Mesh in a geometry consisting of five cylinders
  • Figure 5: Zoomed view of the grid generated for the five-cylinder immersed system, showing details around cylinders 1, 2, 4, and 5.
  • ...and 5 more figures