Numerical simulation of phase transition problems with explicit interface tracking

Abstract

Phase change is ubiquitous in nature and industrial processes. Started from the Stefan problem, it is a topic with a long history in applied mathematics and sciences and continues to generate outstanding mathematical problems. For instance, the explicit tracking of the Gibbs dividing surface between phases is still a grand challenge. Our work has been motivated by such challenge and here we report on progress made in solving the governing equations of continuum transport in the presence of a moving interface by the front tracking method. The most pressing issue is the accounting of topological changes suffered by the interface between phases wherein break up and/or merge takes place. The underlying physics of topological changes require the incorporation of space-time subscales not at reach at the moment. Therefore we use heuristic geometrical arguments to reconnect phases in space. This heuristic approach provides new insight in various applications and it is extensible to include subscale physics and chemistry in the future. We demonstrate the method on applications such as simulating freezing, melting, dissolution, and precipitation. The later examples also include the coupling of the phase transition solution with the Navier-Stokes equations for the effect of flow convection.

High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments

“…We list below only a few examples over the past year (since 2015). Recent applications of WENO schemes can be found in the simulations of astrophysics and geophysics [55,83,137,140,162,172,215,223], atmospheric and climate science [70,181,225], batch chromatographic separation [101], biomolecular solvation [286], bubble clusters in fluids [222], combustion [11,15,24,164,214,268], detonation waves [92,114,145,233], elastic-plastic solids [173], flame structure [261], granular gas [3], hypersonic flows [109], infectious disease models [209], laser welding [174], magnetohydrodynamics [20,166], mathematical finance for solving the Black-Scholes equation [90], multiphase and multispecies flows [13,91,108,110,159,160,239], networks and blood flows [168], ocean waves [28,125], oil storage process [196], rarefi...…”

Computational Simulation of Shock-Bubble Interaction, using a Front-Tracking/Ghost Fluid Method

“…Front-tracking method has been used to simulate two and three-dimensional phase transition phenomena, such as precipitation, dissolution, freezing, and melting problems, with complex and changing interface geometry and topology. In such applications, the interface was propagated by the Lagrangian fronttracking method under the conservation laws of mass or energy coupled with an incompressible Navier-Stokes (Hu et al, 2015). Siguenza et al (2015) investigated a front-tracking immersed boundary method to solve the fluid-structure interactions between a capsule membrane and inner and outer fluids.…”