The dynamic programming interface reconstruction (DPIR) method introduced by Dumas et al.[1] is a volume-preserving and continuous interface reconstruction method. It is a two-step method, which comprises of an optimized step and a correction step. At first, in the optimized step, it minimizes a target function by the dynamic programming method to obtain a continuous interface. Then, it corrects the interface in each mixed cell to preserve the conservative of the volume fraction. However, only the difference of volume fraction is considered, and the interface normal is neglected in the target function. These make it easy to obtain different optimal results in the optimized step, and hence the resulting continuous interfaces always suffer from oscillations (i.e., the ‘wave effects’ [1]). In this paper, to suppress the continuous interfaces’ oscillations in the optimized step and improve its accuracy, we constructed a non-dimensional target function based on the moment-of-fluid method’s objective function, and also proposed a new correction method. Finally, several numerical tests are performed to show the new method’s superiority over the original one of Dumas et al. [1].

Dumas等[1]提出的动态编程接口重构（DPIR）方法。是一种保持体积和连续接口重建的方法。它是两步方法，包括优化步骤和校正步骤。首先，在优化步骤中，它通过动态编程方法最小化目标函数以获得连续接口。然后，它校正每个混合单元中的界面以保留体积分数的保守性。但是，仅考虑了体积分数的差异，而在目标函数中忽略了界面法线。这些使得在优化步骤中容易获得不同的最佳结果，因此，所产生的连续界面总是遭受振荡（即“波效应” [1]）。在本文中，为了在优化步骤中抑制连续界面的振荡并提高其精度，我们基于流体矩法的目标函数构造了无量纲的目标函数，并提出了一种新的修正方法。最后，进行了一些数值测试，以证明新方法优于Dumas等人的原始方法。[1]。