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Investigation of the applicability of the lattice Boltzmann method to free-surface hydrodynamic problems in marine engineering

Abstract : The numerical simulation of the freesurface flows for marine engineering applications is a very challenging issue in the field of computational fluid dynamics (CFD). In this thesis, we propose a solution, which is to use the regularized lattice Boltzmann method (RLBM) with a volume-of-fluid (VOF) based single-phase free-surface lattice Boltzmann (LB) model, and we investigate its feasibility and its reliability. The theoretical insights of the lattice Boltzmann method (LBM) are given at first, through the Hermite expansion and the Chapman-Enskog analysis. From this perspective, the idea of the RLBM is summarized as the Hermite regularization of the distribution functions. On the test-cases of the Taylor-Green vortex and the lid-driven cavity flow, the RLBM is verified to have a 2nd-order accuracy and an improved stability. The adopted free-surface model is then implemented into the RLBM and validated through simulating a viscous standing wave and a dambreak flow problems. It is shown that the regularization not only strongly stabilizes the calculation by reducing spurious pressure oscillations, which is very beneficial for obtaining accurate free-surface motions, but also does not introduce any extra numerical dissipation. Furthermore, a new reconstruction method for the distribution functions at the free-surface is proposed. The present model is more consistent with the RLBM, which provides an effective way for simulating high-Reynoldsnumber free-surface flows in marine engineering.
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Submitted on : Wednesday, November 27, 2019 - 3:46:09 PM
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Weijin Cao. Investigation of the applicability of the lattice Boltzmann method to free-surface hydrodynamic problems in marine engineering. Fluids mechanics [physics.class-ph]. École centrale de Nantes, 2019. English. ⟨NNT : 2019ECDN0011⟩. ⟨tel-02383174⟩

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