A Semi-Lagrangian Meshfree Lattice Boltzmann Method for Incompressible Two-Phase Flows

  • Yu, Hai (Northwestern Polytechnical University)
  • Wang, Xiaodong (Northwestern Polytechnical University)
  • Yang, Shuai (Northwestern Polytechnical University)

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This talk presents an improved Lattice Boltzmann Method (LBM) that integrates the semi-Lagrangian meshfree method with a two-phase lattice Boltzmann (LB) model for simulating incompressible two-phase flow problems. This method involves two LB equations: one is used to solve the Cahn-Hilliard equation for interface capturing, and the other for solving the two-phase Navier-Stokes equations that describe the flow field. Considering the pure convective nature of the LB equations, the semi-Lagrangian meshfree method is adopted to solve these equations. The proposed method is fully meshfree and combines numerous advantages of both meshfree methods and traditional LBM. First, it extends LBM to the meshfree regime, breaking the limitations of uniform meshes. Second, it decouples the time step from the spatial step, thus making it easier to meet the specified accuracy requirements. Third, it fully leverages the advantages of the LB model in interface capturing and parallel computing. Benchmark tests demonstrate that this method exhibits excellent mass conservation performance for both uniform and non-uniform node distributions. Subsequently, the method is applied to several two-phase flow problems. When non-uniform meshfree node distributions are employed, the obtained results are in high agreement with analytical or reference solutions even under extreme simulation conditions.