A well posed and stable canonical evaporation model problem for phase-change in two-phase flows
This provides a rigorous mathematical foundation for validating production codes in two-phase flow simulations, addressing a known bottleneck in ensuring well-posedness and stability.
The authors formulate a well-posed interface formulation for canonical one-dimensional evaporation two-phase model problems (Stefan and Sucking problems) and prove energy stability for high-order accurate numerical discretizations. The work ensures well-posedness and stability for these benchmark problems.
We formulate a well posed interface formulation for canonical one-dimensional evaporation two-phase model problems (the Stefan and Sucking problems) commonly used to validate production codes. We focus on the interface between the vapor and the liquid and derive conditions leading to an energy bound and well-posedness. Next, by mimicking the continuous analysis, we discretize using high order accurate numerical methods on summation-by-parts form, impose the interface conditions weakly and prove energy stability.