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<p>A fully nonlinear potential flow (FNPF) solver has been developed using the Finite Element Method (FEM) to simulate time-domain interactions between free-surface waves and marine structures. The ALE framework is implemented alongside a segment spring analogy-based moving mesh strategy to accurately track evolving free surfaces and moving boundaries of floating bodies. The solver employs a preconditioned conjugate gradient method to efficiently resolve the resulting sparse, symmetric linear system at each time step. Temporal evolution is managed through a standard fourth-order Runge-Kutta scheme, while Chebyshev 5-point smoothing suppresses non-physical saw-tooth instabilities. The solver’s performance and reliability are verified through comprehensive benchmark tests, including free-surface sloshing, nonlinear wave propagation, and wave-structure interactions with submerged or floating bodies. Furthermore, the study explores a modified potential flow model incorporating a quadratic damping term to address viscous effects in gap/moonpool resonance problems.</p>

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An Arbitrary Lagrangian-Eulerian (ALE) Finite Element Potential Flow Solver for Fully Nonlinear Free Surface Flows and Wave-Structure Interactions in the Time Domain

  • 期刊论文

  • 发表日期：

    2026年2月16日

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  • Zhi-wei Song,
  • Pei-qiao Zhu,
  • Jun-jie Zhu,
  • Jun-liang Gao,
  • Ying-yi Liu,
  • Da Chen,
  • Ming-xiao Xie

摘要

A fully nonlinear potential flow (FNPF) solver has been developed using the Finite Element Method (FEM) to simulate time-domain interactions between free-surface waves and marine structures. The ALE framework is implemented alongside a segment spring analogy-based moving mesh strategy to accurately track evolving free surfaces and moving boundaries of floating bodies. The solver employs a preconditioned conjugate gradient method to efficiently resolve the resulting sparse, symmetric linear system at each time step. Temporal evolution is managed through a standard fourth-order Runge-Kutta scheme, while Chebyshev 5-point smoothing suppresses non-physical saw-tooth instabilities. The solver’s performance and reliability are verified through comprehensive benchmark tests, including free-surface sloshing, nonlinear wave propagation, and wave-structure interactions with submerged or floating bodies. Furthermore, the study explores a modified potential flow model incorporating a quadratic damping term to address viscous effects in gap/moonpool resonance problems.