A parallel VOF IB pressure-correction method for simulation of multiphase flows

This paper develops an improved pressure correction method, coupled with volume-of-fluid (VOF) and immersed boundary (IB) methods, to accelerate multiphase flow computations. A momentum interpolation method (MIM) is used to avoid the issue of a checkerboard pressure field on a non-staggered grid system. A transpose-free quasi-minimal residual (TFQMR) method is applied to reduce the CPU time when solving the Poisson equation for the pressure correction procedure. A suitable initial guess for the TFQMR method is investigated to enhance the stability of the matrix solver. The IB method is applied to treat the solid-wall boundary conditions while OpenMP is used to reduce CPU time. Two physical problems - dam breakage and a water wave impacting on a tall structure - are simulated and compared with known data. The improved numerical scheme has CPU speeds at least 8 times faster than the initial numerical scheme for simulating two-phase flows. With regard to the parallel computational efficiency, using six cores with the OpenMP allows the improved scheme to have 77% parallel efficiency. These modifications greatly enhance overall computational accuracy and efficiency.