  In this paper, the compressible immiscible two-phase flow with relaxation is
investigated, this model can be regarded as a natural modification of Jin-Xin
relaxation scheme proposed and developed by S.Jin and Z.P.Xin([Comm.Pure
Appl.Math., 48,1995]) in view of the numerical approximation of conservation
laws. Given any entropy solution consists of two different families of shocks
interacting at some positive time for the standard two-phase compressible Euler
equations, it is proved that such entropy solution is the sharp interface limit
for a family global strong solutions of the modified Jin-Xin relaxation scheme
for Navier-Stokes/Allen-Cahn system, here the relaxation time is selected as
the thickness of the interface, weighted estimation and improved antiderivative
method are used in the proof. Moreover, the simulation results are given by
this modified Jin-Xin relaxation scheme method. Both numerical and theoretical
results show that, the interacting shock waves can pass through the interface
without any effect.
