An improved pressure-equilibrium diffuse interface model for solid-fluid interaction

For solid-fluid interaction, one of the phasic density equations in diffuse interface models is degenerated to a "0 =0" equation when the volume fraction of a certain phase takes the value of zero or unity, because the conservative variables in phasic density equations include volume fractions. The degeneracy can be avoided by adding an artificial quantity of another material into the pure phase. However, non-physical waves are introduced by the artificial treatment. In this paper, an improved pressure-equilibrium diffuse interface model, which is able to treat zero/unity volume fractions, is presented for solid-fluid interaction. In the proposed model, the phasic density equations are replaced by the algebraic relation between phasic densities and inverse deformation gradient tensors. In consequence, the volume fractions and the phasic densities do not appear explicitly in the conservative equations any more. The degeneracy introduced by zero/unity volume fractions are prevented. A flux-splitting based finite difference algorithm suitable for this formulation is then presented. A series of one-dimensional and two-dimensional numerical tests demonstrate that the proposed model can present more accurate results near material interfaces.