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为了寻求更有效的求解不可压缩流体压力的方法,本文基于SHAKE方法构建了一种新的能够模拟宏观自由表面流的ISPH模型。在该模型中,控制方程采用不可压缩Navier-Stokes方程和k-ε湍流方程。在采用SPH表达式和二阶Runge-Kutta时间积分算子对控制方程进行空-时离散的基础上,以水流粒子始终保持初始体积作为约束条件,利用SHAKE方法显式地迭代求解压力项,构建了能够模拟宏观自由表面流的ISPH模型。基于典型溃坝算例,系统比较分析了本文基于SHAKE法的ISPH模型、基于投影法的ISPH模型和VOF模型的模拟效果。结果表明,基于SHAKE法和基于投影法的ISPH模型均能模拟溃坝过程中自由表面水流溅落及水波相撞等大变形物理细节过程,且模拟结果基本相同。与之相比,VOF模型难以模拟该类大变形物理过程,但能够模拟出溃坝过程的主要特征,且水压力分布更趋光滑。与基于投影法的ISPH模型相比,基于SHAKE法的ISPH模型能够完全阻止光滑粒子的非物理穿透现象,数值模拟过程中无任何质量损失。
In order to find a more efficient method to solve the incompressible fluid pressure, a new ISPH model that can simulate macroscopic free surface flow is constructed based on the SHAKE method. In this model, the governing equations use incompressible Navier-Stokes equations and k-ε turbulence equations. Based on the SPH expression and the second-order Runge-Kutta time integral operator, the control equations are spatially-temporally discretized, and the initial particle volume of water particles is kept as the constraint condition. The pressure term is explicitly iteratively solved by SHAKE method to construct the An ISPH model that simulates a macro free surface flow. Based on the typical dam-break example, the system compares and analyzes the ISPH model based on SHAKE method, the ISPH model based on projection method and the simulation effect of VOF model. The results show that both the SHAKE method and the ISPH model based on the projection method can simulate the large-scale physical details such as free-surface water-flow splashing and water-wave collision in the process of dam breaching, and the simulation results are basically the same. In contrast, VOF model is difficult to simulate this kind of large deformation physical process, but it can simulate the main features of dam break process, and the water pressure distribution is smoother. Compared with the ISPH model based on the projection method, the SHAKE-based ISPH model can completely prevent the non-physical penetration of smooth particles without any quality loss in the numerical simulation.