Liquid-vapor phase transition: Thermomechanical theory, entropy stable numerical formulation, and boiling simulations

We develop a new continuum mechanics modeling framework for liquid-vapor flows, with particular focus on the van der Waals fluid. By invoking microforce theory, the Coleman-Noll procedure is generalized to derive consistent constitutive relations in the presence of non-local effects. A new thermodynamically consistent algorithm for the van der Waals model is designed, using functional entropy variables and a new temporal scheme employing a family of new quadrature rules. We show that the resulting fully discrete scheme is unconditionally stable in entropy and second-order time-accurate. Isogeometric analysis is utilized for spatial discretization. The analytical properties of the formulation are corroborated by benchmark problems. Three sets of application problems are simulated to demonstrate the capability of the model and the algorithm. Our methodology provides a particularly useful predictive tool for boiling flows. (C) 2015 Elsevier B.V. All rights reserved.