Simulations of multidimensional interfacial flows by an improved volume-of-fluid method

In this article we present a 2D and 3D practical interface tracking algorithm to reconstruct and advect the interfaces of interfacial flows. The improved volume-of-fluid (VOF) method in this work is composed of three major components: namely (1) the modified piecewise linear interface calculation (PLIC) based interfacial reconstruction; (2) the Lagrangian split fluid advection and (3) redistribution of volume fraction. Most advanced VOF methods employed by the PLIC technique have faced some problems to extend from 2D to 3D study, because the increase in complexity of the geometry primitives involved has made implementations excessively difficult and ultimately infeasible. The improved algorithm in this study is used to capture the interface of the immiscible fluids which are applicable both in 2D and 3D spaces. A computationally efficient and second-order accurate interface reconstruction method is applied. The normal estimation of the interface is approximated by combining the centered column scheme and the Youngs' method. Besides, a linear mapping technique is implemented to improve the efficiency of numerical simulations with regard to the approximation of capturing the interface. The sequence of the Lagrangian advection in each direction is considered to restrain the fragmentation caused by the strong interface deformation as the fluids propagate. It is significant to note that the method can be accurately accomplished by a regular structured mesh without any geometrical modifications such as boundary fitted grids. Next, the mass conservation is numerically assessed, thus allowing computations to reach the machine precision. The computational results include widely used benchmarks in 2D and 3D cases, such as the solid-body translations and rotations, the swirled single vortex and the deformation fields of fluid body. Good results are obtained through some numerical tests by using present algorithm as comparing with other numerical solutions.