基于物理碰撞的边界处理方法

A method to handle boundary based on physical collision

传统的光滑粒子流体动力学(smoothed particle hydrodynamics,SPH)方法在模拟流体时,核函数一致性的局限性导致在边界处产生较大的数值耗散,降低了边界处粒子的密度值及压强值的计算精度,导致流体体积的错误变化,进而影响模拟效果。文章提出一种SPH方法和物理碰撞相耦合的方法,对于非靠近边界的粒子,用SPH方法计算它们的各种属性;对于靠近边界处的粒子,赋予它们静止密度,使用纯粹的物理弹性碰撞来计算其速度和位置。在此过程中,文章给出了一种有效区分靠近边界的粒子和非靠近边界的粒子的方法;此外还加速了Marching Cubes算法。通过对比实验结果发现,该文方法可以准确计算流体的密度及压强,使得流体体积更加地接近精确值。

In flow simulation, the unity of the kernel function of the traditional smoothed particle hydrodynamics（SPH） method usually causes serious numerical dissipation at boundaries, which reduces the calculating accuracy of particle’s density and pressure at boundaries. These influences lead to incorrect change of the volume of fluid, and then cause unrealistic simulation. In this paper, a method to solve the problem aforementioned using the combination of the SPH method and physical collision is given： the properties of particles far from the boundary will be calculated by the SPH method, and particles near the boundary will be given a static density, and their velocities and positions will be calculated by physical collision. During this process, a method to distinguish particles near or far from the boundary is proposed. In addition, Marching Cubes algorithm is accelerated. Compared with the simulation results, more accurate values of density and pressure are obtained by using the proposed method, which makes the volume of fluid get closer to exact value.