An improved continuity-preserving interface reconstruction method for multi-material flow

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]. (C) 2021 Elsevier Ltd. All rights reserved.