A very robust MMALE method based on a novel VoF method for two-dimensional compressible fluid flows.

The Volume of Fluid (VoF) method stands out as a widely utilized tool for capturing interfaces in the numerical simulation of multimaterial fluid flow. Numerous efforts have been invested in enhancing its accuracy and efficiency, including the development of analytic reconstruction methods. Despite these advancements, there exists a continued need for further improvements in the accuracy, efficiency, and robustness of the VoF method in practical applications. In the conventional VoF method, information from neighboring cells is crucial for computing the normal vector of the interface in each multimaterial cell, requiring data from as many as 26 neighboring cells in 3D VoF methods. This paper introduces a novel VoF method named SVoF, which departs from traditional approaches by eliminating the necessity for information from neighboring cells. In the SVoF method, the data provided for interface reconstruction in each multimaterial cell consists of the volume fractions of fluids in several subcells within the cell itself. Initially, these data are determined by the initial conditions. In MMALE methods, these data can be updated through a closure model for multimaterial cells in each Lagrangian stage and remapped in each subsequent remapping stage. The determination of the normal vector of the linear interface in SVoF is achieved through an optimization procedure. The objective function of this procedure is the sum of the squares of the differences between the given volume fractions and the reconstructed volume fractions of the reference fluid in specific subcells. The optimization procedure is solved using an improved quadratic fit golden section algorithm. Similar to traditional VoF methods, the intercept of the linear interface is calculated by precisely matching the given volume fraction of the reference fluid throughout the entire multimaterial cell. The SVoF method is characterized by its ease of coding and implementation, making it suitable for interface reconstruction in multimaterial cells containing three materials. Building upon the SVoF method, a new cell-centered MMALE method is developed, showcasing robustness. This new MMALE method utilizes Tipton's pressure relaxation model for the closure of multimaterial cells and leverages the SVoF method for interface reconstruction. Numerical results demonstrate that the SVoF method can precisely reproduce linear interfaces, approaching second-order accuracy, and that this new MMALE method exhibits significant robustness. • A novel VoF method (SVoF) that doesn't require information from neighboring cells. • SVoF requires the volume fractions of fluids in multiple subcells within each multimaterial cell. • SVoF is applicable for interface reconstruction in multimaterial cells containing three distinct materials. • SVoF precisely reproduces linear interfaces and is straightforward to code and implement. • MMALE combined with SVoF demonstrates greater robustness compared to the existing MMALE coupled with MoF. [ABSTRACT FROM AUTHOR]