改进的SPH方法的精度问题研究

Research on the accuracy of improved SPH method

传统的SPH方法不能很好的模拟流体的运动状态,其原因是核函数的边界截断导致流体边界处的精度较低,很难得到收敛和精确的结果。而DSPH、KGF-SPH和FPM-SPH作为改进的SPH方法,具有较高的计算精度。通过常函数、线性函数等拟合验证传统的SPH方法和改进的SPH方法的零阶一致性和一阶一致性。通过溃坝问题和方形液滴震荡两个经典算例验证改进的SPH方法的精度问题。结果显示,改进的SPH方法能够达到一阶一致性,改进的SPH方法模拟效果良好,进一步证实了改进的SPH方法能够有效地提高模拟的计算精度和数值稳定性。

The traditional SPH method cannot simulate the motion state of the fluid well,because the boundary truncation of the kernel function leads to low precision at the fluid boundary,and it is difficult to get convergence and accurate results.As improved SPH methods,DSPH,KGF-SPH and PFM-SPH have higher calculation accuracy.The zero-order consistency and first-order consistency of the traditional SPH method and the improved SPH method are verified by constant function and linear function,and the accuracy of the improved SPH method is verified by two classical examples of the square droplet oscillates and dam break.The improved SPH method has good simulation results,which further proves that the improved SPH method can effectively improve the calculation accuracy and numerical stability of the simulation.