不可压流体自由表面流动的SPH数值模拟

MODELING FREE SURFACE FLOW OF INCOMPRESSIBLE FLUID USING SPH

根据SPH方法的原理提出了一套模拟流体自由表面流动的方法,场变量及其导数通过核函数插值求取,不需进行差分,也不需要网格,时间积分采用分数步长法,避免了不可压条件带来的压力计算不稳定问题。对流项通过粒子的运动求解,完全消除了数值扩散和自由表面模糊问题。可以模拟飞溅、融合等复杂自由表面现象,并对水坝坍塌这一典型自由表面流动问题进行了模拟,模拟结果与试验吻合良好。

A Lagrange particle method based on SPH(Smoothed particle hydrodynamics) is presented to simulate the free surface incompressible fluid flow. Field variables and their derivatives are evaluated through interpolation of kernel function without need of any mesh. A fractional step method is used in time integration, which stabilizes the computation of pressure. Owing to the virtue of Lagrangian formulation, the smearing of free surface resulting from the numerical diffusion for convective terms is eliminated completely. The method is applied to simulate a benchmark breaking dam problem. The simulation results agree well with the experimental results although fragmentation and coalescence take place.