An adaptive level-set method with enhanced volume conservation for simulations in multiphase domains.

International audienceWhile implicit interface methods such as the Level-Set method have the main advantage of avoiding explicit interface meshing, they raise important volume conservation issues that can be handled by local mesh refinement. This refinement is then performed multiple times throughout the simulation in order to follow the interface. Nevertheless, mesh adaptation itself is a process that generates a volume conservation problem due to field transfer. In this work, multiphase simulations are addressed using a new Lagrangian Level-Set method that relies on an automatic mesh motion and topological mesh adaptation procedure. Remeshing is hence activated only when element flipping is detected. This procedure is extended in order to take into account local phase distributions during remeshing, so that volume conservation can be controlled [2]. This method relies on a robust Level-Set reinitialization technique, also developed in this work [1]. This constraint on volume conservation is automatically relaxed when necessary in order to take into account complex topological events such as apperance, disappearance, and coalescence of objects during the simulation. Numerical results show that the proposed method is competitive in terms of cost and accuracy, with respect to standard Eulerian and Lagrangian Level-Set methods, while still enabling large displacements and deformations. Some examples concerning the modeling of evolutive microstructures will be detailed. Références : [1] M. Shakoor, B. Scholtes, P.-O. Bouchard, and M. Bernacki. An efficient and parallel level set reinitialization method - application to micromechanics and microstructural evolutions. Applied Mathematical Modelling, 39(23-24) :7291–7302, 2015. [2] M. Shakoor, P.-O. Bouchard, and M. Bernacki. An adaptive level-set method with enhanced volume conservation for simulations in multiphase domains. International Journal for Numerical Methods in Engineering, Volume 109, Issue 4, 27 January 2017, 555–57