In this article, a δ⁺-LES-SPH model is presented to study the generation and propagation of impulse waves. In this model, a density diffusion term is added to the continuity equation to eliminate the numerical high-frequency oscillation of the pressure field. A particle shifting technique is introduced and modified in the motion equation to improve the accuracy and robustness of the smoothed particle hydrodynamics (SPH) model. The physical viscosity term and the turbulence viscosity term based on the large eddy simulation (LES) are used in the momentum equation to calculate the viscous force. To predict the rigid slide motion more effectively, we propose a rigid slide motion model that considers friction in the δ⁺-LES-SPH frame. The δ⁺-LES-SPH code was implemented in Fortran 90, and OpenMP programming technology was used to improve the calculation efficiency. Subsequently, this parallel SPH code was used to simulate subaerial and submarine rigid landslides in 2-D and more realistic 3-D applications. The SPH results were compared with the experimental data and other numerical results. The results show that the proposed model has a good convergence and less numerical dissipation. Satisfactory results were obtained for the rigid slide motion, wave generation, and long-distance propagation.

在本文中，提出了一个δ ⁺ -LES-SPH模型来研究脉冲波的产生和传播。在该模型中，将密度扩散项添加到连续性方程中，以消除压力场的数值高频振荡。在运动方程中引入并修改了粒子移位技术，以提高平滑粒子流体动力学（SPH）模型的准确性和鲁棒性。动量方程式中使用了基于大涡模拟（LES）的物理粘度项和湍流粘度项来计算粘性力。为了更有效地预测刚性滑动运动，我们提出了一种刚性滑动运动模型，该模型考虑了δ ⁺ -LES-SPH框架中的摩擦。δ ⁺-LES-SPH代码在Fortran 90中实现，并且使用OpenMP编程技术提高了计算效率。随后，该并行SPH代码用于模拟二维和更实际的3-D应用中的海底和海底刚性滑坡。将SPH结果与实验数据和其他数值结果进行了比较。结果表明，该模型收敛性好，数值耗散小。刚性滑动，波浪产生和长距离传播都获得了令人满意的结果。