K2_SPH方法及其对二维非线性水波的模拟

K2_SPH Method and Application for 2D Nonlinear Water Wave Simulation

K2_SPH方法通过泰勒级数展开和联立求解积分方程组的办法得到具有二阶精度的核近似方法.随着核近似精度的提高,K2_SPH需要对一些关键数值技术进行改进才能成功模拟非线性水波问题,例如自由表面边界和固壁边界.通过与传统SPH方法计算结果比较,K2_SPH方法在非线性自由表面计算精度和整个粒子系统中有关变量分布都有显著提高.

Smoothed particle hydrodynamics is a Lagrangian meshless partilcle method. It gets superiority in simulation of free surface flow and large deformation problems. But low accuracy of kernel approximation becomes an obstacle for widely applications as particles are distributed disorderly or near a boundary. Adopting Taylor expansion and solving integral equation matrix, a second order kernel approximation method, namely K2_SPH is obtained and discussed. With improvement of kernel approximation, improved numerical techniques are adopted, such as free surface boundary and solid boundary. They are very important for K2_SPH method. With comparison of standard SPH for nonlinear water wave simulation, K2_SPH improves obviously in free surface simulation and distribution of some variables in total particle system.