An Improved Pressure-Equilibrium Diffuse Interface Model for Solid-Fluid Interaction (Communications in Computational Physics, 2019)
For solid-fluid interaction, one of the phasic density equations in diffuseinterface models is degenerated to a "0 = 0" equation when the volume fraction of acertain phase takes the value of zero or unity, because the conservative variables inphasic density equations include volume fractions. The degeneracy can be avoided byadding an artificial quantity of another material into the pure phase. However, nonphysical waves are introduced by the artificial treatment. In this paper, an improvedpressure-equilibrium diffuse interface model, which is able to treat zero/unity volumefractions, is presented for solid-fluid interaction. In the proposed model, the phasicdensity equations are replaced by the algebraic relation between phasic densities andinverse deformation gradient tensors. In consequence, the volume fractions and thephasic densities do not appear explicitly in the conservative equations any more. Thedegeneracy introduced by zero/unity volume fractions are prevented. A flux-splittingbased finite difference algorithm suitable for this formulation is then presented. Aseries of one-dimensional and two-dimensional numerical tests demonstrate that theproposed model can present more accurate results near material interfaces.