The eXtreme Mesh deformation approach (X-MESH) for the Stefan phase change model

Towards a sharper phase-field method: A hybrid diffuse–semisharp approach for microstructure evolution problems

“…Quantities referring to the sharp interface are here denoted by a symbol with a hat. Direct computational (e.g., finite-element) treatment of the microstructure evolution problem within the sharp-interface framework is not straightforward because it would require remeshing to ensure that the mesh matches the evolving microstructure at each time instant (and possibly at each iteration), see [44] for a recent development towards this goal. A feasible approach to model moving interfaces is to adopt a diffuse-interface approximation independent of the spatial discretization, which is discussed next.…”

X-Mesh: A new approach for the simulation of two-phase flow with sharp interface

“…The idea behind the X-Mesh method [9] is to deform a mesh with continuous node movements to constantly match the interfaces of interest, even in the case of topological changes of the fluids domains. The mesh however keeps a fixed topology.…”

“…Any preconditioner will solve this problem. In this paper, we proceed in the same fashion as in [9]. We simply limit the maximum value of λ 3 by limiting the minimum value of the area of degenerated triangles.…”

“…Another ingredient of the algorithm is to move the vertices only upstream of the front. This allows the relay process to run smoothly, without having downstream vertices moving in the opposite direction of the front movement and creating some kind of traffic jam [9]. Finally, when a vertex of the front has passed the relay to another vertex, it progressively returns to its initial position which allows to maintain a quality mesh upstream of the front.…”

“…Recently, we developed a tracking method called X-Mesh that had the following specifications: i) to be sharp, ii) to work on a fixed topology mesh and iii) to allow large topological changes of the interfaces. The first X-Mesh paper was dealing with the immaterial interface computation of phase-changes using the Stefan model [9]. This paper aims to develop X-Mesh in the context of material interfaces and in particular to solve two-phase flow problems.…”