Implicit ISPH Method for Unified Free-Surface and Non-Darcy Flow Simulation

  • Takahashi, Kazuma (Tohoku University)
  • Tsuji, Kumpei (Tohoku University)
  • Asai, Mitsuteru (Kyushu University)

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Seepage failures in levees and ground foundations induced by recent extreme weather events are causing severe damage worldwide. To investigate the mechanisms of such failures and to develop effective countermeasures, numerical analysis provides a powerful tool. These problems require a unified simulation framework capable of describing both free-surface flows, such as overflow, and seepage flow within the ground. Moreover, considering large-scale domains such as levees and long-duration phenomena ranging from minutes to hours, computational efficiency is a critical requirement. The Incompressible Smoothed Particle Hydrodynamics (ISPH) method has previously been applied to the Darcy–Forchheimer–Brinkman (DFB) equation, providing a unified formulation for free-surface and seepage flows. This semi-implicit ISPH-based approach has been shown to be robust and reliable through benchmark validations. However, its application to real-scale problems involving large spatial domains and long simulation times remains challenging. In particular, strict time-step constraints lead to increased computational cost and may also cause numerical instability, which limits its practical applicability. In this study, an implicit ISPH method is introduced for the Darcy–Forchheimer–Brinkman (DFB) equation by modifying the predictor step so that both the drag terms and the Brinkman term are treated implicitly. This formulation alleviates the severe time-step restrictions inherent in the conventional semi-implicit ISPH scheme and enables stable computations with significantly larger time increments. The validity and effectiveness of the proposed method are demonstrated through numerical experiments of two-dimensional Poiseuille flow and seepage flow. Furthermore, simulations involving complex free-surface deformations show good agreement with available experimental data, confirming the applicability of the method to practical seepage and overflow problems.