Interface pressure calculation based on conservation of momentum for front capturing methods

A new method for the calculation of interface pressure for front capturing methods is developed. This method is based on the calculation of the pressure force at each interfacial cell face using the exact pressure due to the portion of the cell face that is occupied by each fluid. Special formulations for the pressure in the interfacial cells are derived for different orientations of an interface. This method (referred to as pressure calculation based on the interface location (PCIL)) is applied to the time evolution of a two-dimensional initially stagnant liquid drop in a gas, as well as, a gas bubble in liquid (gravity effects are not considered). A two-fluid, PLIC-VOF method is used to simulate the flow numerically. Both the continuum surface force (CSF) and the continuum surface stress (CSS) methods are used. A wide range of Ohnesorge numbers and density and viscosity ratios of two fluids are tested. It is shown that the new method reduces the spurious currents by up to three orders of magnitude for the cases tested.