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Phase-transition problems pose significant challenges to the numerical method. Accurately resolving the moving domain, involving arbitrary topology changes, is one of the main problems. We develop a numerical method for phase-change problems involving rarefied gases.

In rarefied gas dynamics, classical models like Fourier's law cannot be used due to insufficient collisions and the lack of equilibrium. Extended gas dynamics models, such as moment approximations in kinetic theory, augment traditional continuum mechanics and include more variables and equations to describe the state of the gas, resulting in increased complexity of the equations. Similarly, the phase interface is subject to jump conditions that couple interface velocity, local equilibrium, and non-equilibrium variables in a possibly discontinuous way, triggering boundary layer effects that shape the bulk solution. Together with the nonlinear coupling of the evolving domain and the physical field equations, phase transitions in rarefied gas dynamics pose a significant challenge to numerical discretizations. We work on a mesh-conforming interface method based on an implicit representation of the interface, using standard finite elements and the level-set method with exact remeshing. Remeshing at every time step yields highly accurate and robust representations of the individual domain boundaries and the phase interface, allowing the interface conditions to be imposed directly and thus avoiding interpolation errors. Moreover, the field equations can be implemented without modification, using standard solvers. The finite element solver and the meshing tool in our framework are exchangeable and adaptable.

The gif shows an exemplary interface problem highlighting the robustness of the method to deal with arbitrary domain deformations. The method captures merging, separation and removal of interface segments. Furthermore, boundary contact is supported. Temperature contours are superimposed by heat flux glyphs; the interface is highlighted in white.

Preprint available at http://dx.doi.org/10.2139/ssrn.5163120

Contact: Donat Weniger