基于黎曼求解器的SPH算法及其应用

SPH algorithm based on Riemann solver and its application

基于传统光滑粒子流体动力学方法(SPH)进行数值模拟时,在边界处存在压力和速度震荡,甚至导致求解失败。为准确求解SPH方程式中的粒子的物理粘性,减小数值耗散,将黎曼求解器纳入SPH格式中,通过重整化过程对连续性方程中的梯度算子进行了校正。通过一系列经典算例的数值模拟结果表明,基于黎曼求解器的SPH算法能够准确的模拟液体的流动,且具有良好的准确性和鲁棒性。

In the numerical simulation based on the traditional smooth particle fluid dynamics(SPH)method,there are pressure and velocity oscillations at the boundary,and even the solution fails.In order to accurately solve the physical viscosity of the particles in the SPH equation and reduce the numerical dissipation,the Riemann solver is incorporated into the SPH scheme,and the gradient operator in the continuity equation is corrected by renormalization.Through a series of classical examples,the numerical simulation results show that the SPH algorithm based on Riemann solver can accurately simulate the flow of liquid,and has good accuracy and robustness.