Two-phase flow simulation using the X-Mesh approach
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Accurately modelling boundaries and interfaces in motion is a difficulty in many computational mechanics problems. Recently, we have proposed a new idea, the eXtreme mesh deformation approach (X-Mesh), to describe physical interface at low cost [1]. In this approach, a deforming mesh with fixed topology and continuous motion of nodes permanently adapts to the interfaces of interest, even in the case of topological changes of the fluid domains. To achieve this, X-Mesh allows zero-measure elements, i.e. a triangle can be deformed into an edge or even a point. This allows the mesh to deform in a time-continuous manner and provides the interface transfer. The interface is transferred from one node to another node at the same position, allowing interface propagation in the manner of a relay race. In a previous work we proposed this approach coupled with a level set description of the interface [2]. A much-praised advantage of the level set method is the way in which it naturally allows the topology of the two phases to change. The phases automatically merge when there is only one element separating them. This feature makes it easier to implement this type of method, where topological changes do not require any particular attention. The price to pay is that it is not possible to preserve flow features smaller than the mesh size. In this work we propose to use an oriented list of Lagrangian particles to track the interface. This description of the interface allows us to keep smaller features of the phases with coarse meshes. The results are validated through a serie of testcases including Rayleigh-Taylor instability, bubble rise, dambreak and sloshing. [1] N. Moës, J-F. Remacle, J. Lambrechts, B. Lé and N. Chevaugeon. The eXtreme Mesh deformation approach (X-MESH) for the Stefan phase change model. Journal of Computational Physics 477, 2023 [2] A. Quiriny, J. Lambrechts, N. Moës and J-F Remacle. X-Mesh: A new approach for the simulation of two-phase flow with sharp interface https://doi.org/10.48550/arXiv.2302.03983, 2023