ReALE: A Reconnection Arbitrary-Lagrangian–Eulerian method in cylindrical geometry

This paper deals with the extension to the cylindrical geometry of the recently introduced Reconnection algorithm for Arbitrary-Lagrangian–Eulerian (ReALE) framework. The main elements in standard ALE methods are an explicit Lagrangian phase, a rezoning phase, and a remapping phase. Usually the new mesh provided by the rezone phase is obtained by moving grid nodes without changing connectivity of the underlying mesh. Such rezone strategy has its limitation due to the fixed topology of the mesh. In ReALE we allow connectivity of the mesh to change in rezone phase, which leads to general polygonal mesh and permits to follow Lagrangian features much better than for standard ALE methods. Rezone strategy with reconnection is based on using Voronoi tesselation machinery. In this work we focus on the extension of each phase of ReALE to cylindrical geometry. The Lagrangian, rezone with reconnection and remap phases are revamped to take into account the cylindrical geometry. We demonstrate the efficiency of our ReALE in cylindrical geometry on series of numerical examples.