Abstract
Numerical simulation of multi-fluid flows presents a challenge, because the fluid properties are discontinuous across the fluid interface. To overcome this difficulty, fluids of different properties are identified through the use of a continuous field variable — the color function. The color function assigns a unique constant to each fluid. Interfaces between different fluids are distinct due to sharp gradients of the color function. The evolution of the interfaces is governed by the convective equation of the color function, while the fluid motion is governed by the incompressible Navier—Stokes equations. Therefore, conventional approaches are composed of two distinct methodologies, namely, a flow equation solver which is usually based on staggered grids, operator-splitting or projection methods; and a pure convection equation solver to identify the material by Lagrangian or upwind methods. Since these two totally different numerical techniques must be incorporated together, simulating two-fluid flows is regarded as a very complex problem.
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