A Numerical Approach for the Existence of Dissipative Weak Solutions to a Compressible Two-fluid Model

Abstract

As an extension of the recent work of Novotný et al. (J Elliptic Parabol Equ 7:537–570 2021), we study the dissipative weak solutions to a compressible two-fluid model system describing the time evolution of two fluid flows sharing the same velocity field in multi-dimensional spaces. We prove the existence of dissipative weak solutions alternatively via a finite volume approximation. Further, we apply the weak–strong uniqueness principle to show the convergence of the finite volume approximation towards the strong solution on the lifespan of the latter.