Abstract
This work focuses on the formulation of a four-equation model for simulating unsteady two-phase mixtures with phase transition and strong discontinuities. The main assumption consists in a homogeneous temperature, pressure and velocity fields between the two phases. Specifically, we present the extension of a residual distribution scheme to solve a four-equation two-phase system with phase transition written in a non-conservative form, i.e. in terms of internal energy instead of the classical total energy approach. This non-conservative formulation allows avoiding the classical oscillations obtained by many approaches, that might appear for the pressure profile across contact discontinuities. The proposed method relies on a finite element based residual distribution scheme which is designed for an explicit second-order time stepping. We test the non-conservative residual distribution scheme on several benchmark problems and assess the results via a cross-validation with the approximated solution obtained via a conservative approach, based on a HLLC scheme. Furthermore, we check both methods for mesh convergence and show the effective robustness on very severe test cases, that involve both problems with and without phase transition.
Bacigaluppi, Paola