【摘要】 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。更多还原

【Abstract】 In this study,to explore an effective solving pressure method,an ISPH model for macro free-surface flow based on the SHAKE method has been developed. The fluid flow is governed by incompress-ible Navier-Stokes equations and k-ε equations. Based on the SPH spatial discretization,the explicit two-order time integrator is used to the governing equations and then the SHAKE is used to explicitly solvepressure by solving the nonlinear equations of conserving particle initial volumes. Dam-break cases with dryand wet beds are simulated by the developed ISPH model,the ISPH model based on the projection meth-od and the VOF model. The simulated results show that the developed ISPH model has a more ability ofsimulating large deformation and physical details such as splashing and two waves colliding,so does thesame results for the ISPH model based on the projection method,but less the smooth pressure. By con-trast,the VOF model can simulate the main characteristic of flow and has a more smooth pressure distribu-tion. Compared with the ISPH model based on the projection method,the developed model presents a bet-ter mass conservation,that is,the developed model can completely prevent particle’s non-physical leavingcomputational domain.更多还原