Compressive advection and multi-component methods for interface-capturing

Summary This paper develops methods for interface‐capturing in multiphase flows. The main novelties of these methods are as follows: (a) multi‐component modelling that embeds interface structures into the continuity equation; (b) a new family of triangle/tetrahedron finite elements, in particular, the P1DG‐P2(linear discontinuous between elements velocity and quadratic continuous pressure); (c) an interface‐capturing scheme based on compressive control volume advection methods and high‐order finite element interpolation methods; (d) a time stepping method that allows use of relatively large time step sizes; and (e) application of anisotropic mesh adaptivity to focus the numerical resolution around the interfaces and other areas of important dynamics. This modelling approach is applied to a series of pure advection problems with interfaces as well as to the simulation of the standard computational fluid dynamics benchmark test cases of a collapsing water column under gravitational forces (in two and three dimensions) and sloshing water in a tank. Two more test cases are undertaken in order to demonstrate the many‐material and compressibility modelling capabilities of the approach. Numerical simulations are performed on coarse unstructured meshes to demonstrate the potential of the methods described here to capture complex dynamics in multiphase flows. Copyright © 2015 John Wiley & Sons, Ltd. We present theory and apply an interface‐capturing method for multiphase flow problems in 2D and 3D with emphasis on the use of adaptive unstructured finite element meshes. The method is mass‐conserving and able to ensure that key forces such as buoyancy and hydrostatic pressure are exactly balanced. In addition, arbitrary numbers of phases with arbitrary equations of state can be modelled as demonstrated here.