This paper proposes an effective density correction method to improve the accuracy and reliability of smoothed particle hydrodynamics (SPH) simulations. The density field calculated in the SPH procedure is automatically corrected by a new density interpolation adopting shape functions, which is individually applied to each particle. The proposed method makes the density field smoother, effectively reducing unphysical oscillations and peaks in density and pressure, with small additional computations. Unlike previous methods, the new density correction method does not result in flattened solutions, even when used too frequently or for a long time. The proposed method can be easily applied to both 2D and 3D flow analysis. The performance of the proposed method is demonstrated through various numerical examples including violent free surface flows. In particular, comparisons with the Shepard interpolation, the MLS interpolation, and δ-SPH are studied.

本文提出了一种有效的密度校正方法，以提高平滑粒子流体动力学（SPH）模拟的准确性和可靠性。通过采用形状函数的新密度插值，可以自动校正SPH过程中计算出的密度场，该函数分别应用于每个粒子。所提出的方法使密度场更加平滑，只需很少的额外计算，即可有效地减少非物理振荡以及密度和压力的峰值。与以前的方法不同，即使太频繁或长时间使用，新的密度校正方法也不会使解决方案变平。所提出的方法可以轻松地应用于2D和3D流量分析。通过各种数值示例（包括剧烈的自由表面流动）证明了该方法的性能。