Numerical Simulation of Low-Speed Two Phase Flows Based on Preconditioning

This paper first applies flux vector type splitting method based on numerical speed of sound for computing incompressible single and multi-fluid flows. Here, a preconditioning matrix based on Chorin’s artificial compressibility concept is used to modify the incompressible multi-fluid Navier-Stokes Equations to be hyperbolic and density or volume fraction independent. The current approach can reduce eigenvalues disparity induced from density or volume fraction ratio and enhance numerical stability. Also, a simple convection-pressure flux-splitting method with high-order essentially non-oscillatory (ENO) type primitive variable extrapolations coupling with an ENO-MUSCL type volume fraction recompressed reconstruction within a mesh cell is used to maintain the preservation of sharp interface evolutions in multi-fluid flow simulation. Benchmark tests including a solid rotation test of a notched 2D cylinder, the evolution of spiral and rotational shapes of deformable circles, a dam breaking problem, the Rayleigh-Taylor instability and the cavitated flow problems are chosen to validate the current incompressible multi-fluid methodology.