Mixtures of phase transforming fluids and gases: Phase field model and stabilized isogeometric discretization

Abstract

Liquid–vapor phase change in the presence of non-condensable gases is a classical problem, which continues to challenge continuum modeling. Here, we propose a new model based on the phase field method, which describes the dynamics of the non-condensable gas, phase change and flow simultaneously. The model is built by extending van der Waals and Korteweg’s theory for phase-transforming mixtures. The model equations have fourth order partial differential operators which presents significant challenges to standard spatial discretization methods. In addition, the isentropic form of the model equations is not hyperbolic at the liquid–gas interface, which inhibits the direct application of most algorithms for systems of hyperbolic equations. We propose a novel numerical scheme based on Isogeometric Analysis and the Taylor–Galerkin method, and also implement a residual based discontinuity capturing scheme. We show numerical results, at micron length scales, to study the accuracy and stability of our algorithm. We study the flow of a shock wave past a liquid droplet to test our numerical algorithm when steep gradients are present in the solution. Finally, we use the model to study the problem of gas–vapor bubble collapse near a solid wall.