The Level Set Interface-Tracking Model Coupled to SPH Method

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LMH Laboratory for Hydraulic Machines 1st SPHERIC Workshop - Rome - May 10-12, 2006 The Level Set Method The two-phase two phase mixture is as a single fluid Density, viscosity are smoothed across the interface The LS marker function is continuous and it is set to the signed minimum distance to the interface Reasons for using the LS function: Minimal numerical diffusion since the function is continuous across across the interface, with ∇φ = 1 Easy to interpolate phase properties across the interface in the two-fluids two fluids formulation -d Phase 2 Phase 1 +d d=0 4/14
LMH Laboratory for Hydraulic Machines 1st SPHERIC Workshop - Rome - May 10-12, 2006 The Level Set Method Non-conservative Non conservative form of Level Set equations: ∂ φ + u ⋅∇ φ = 0, ∂t ∂ φ + sign( φ ( ) 0) ∇φ − 1 = λ ∇φ δε ( φ) ∂τ Interpolation of phase properties across the numerical interface: interface ρ( x, t) = ρ + ( ρ − ρ ) H 1 μ( x, t) = μ + ( μ − μ ) H 1 1 1 2 2 ε ε ( φ( x, t) ) ( φ( x, t) ) ρ μ 1, 1 n ρ μ 2, 2 φ = 0 • Straightforward to couple Level Set and SPH • LLSM = best mass conservation of the existing LS 5/14
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The Level Set Interface-Tracking Model Coupled to SPH Method

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