A fully conservative sharp-interface method for compressible multiphase flows with phase change

Abstract

In this paper, a fully conservative sharp-interface method is developed for compressible multiphase flows with phase change. To enforce conservation, the coupling between two different phases is achieved via the interfacial fluxes, which are determined by solving a general Riemann problem with phase change. In addition, thermodynamical consistency is guaranteed by taking account of latent heat in the phase-change Riemann problem. This is efficiently and robustly solved by a novel approximate Riemann solver, where the complex eight-dimensional root-finding procedure required in the exact Riemann solver is simplified to solely iterating the mass flux. Compared to the existing methods, the present approximate Riemann solution consists of four waves, at which the jump conditions are imposed strictly to enforce the conservation of mass, momentum, and energy. Furthermore, for the evaluation of the mass flux, through numerical simulations and theoretical analysis, we have demonstrated that the adjacent states of a phase interface should be used to ensure numerical consistency, which, to our knowledge, has not been reported in the literature. Various numerical examples, including the phase-change Riemann problem, the oscillating droplet problem, and the shock-droplet interaction problem, are simulated to validate the present method. The numerical results are in good agreement with the exact solutions and the previous simulations. It is shown that, with the present method, the phase change effects in compressible multiphase flows are well resolved with conservation strictly preserved.