Adaptive reconnection-based arbitrary Lagrangian Eulerian method: A-ReALE

W present a new adaptive reconnection-based arbitrary Lagrangian Eulerian: A-ReALE method. The main elements in a A-ReALE method are: An explicit Lagrangian phase on arbitrary polygonal mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined number of mesh cells, their location and connectivity (it is based on using Voronoi tessellation) in rezoned mesh is changing and a remapping phase in which the Lagrangian solution is transferred onto the new grid. The rezoning strategy was based on following design principles: Using monitor (error indicator) function based on Hessian of some flow parameter(s), which is measure of interpolation error; using equi-distribution principle for monitor function as criterion for creation of adaptive mesh; using weighted centroidal voronoi tessellation as a tool for creating adaptive mesh; modification of the raw monitor function-we scale it to avoid very small and very big cells and smooth it to create smooth mesh and allow to use theoretical results related to weighted centroidal voronoi tessellation. In A-ReALE both number of cells and their locations allowed to change at rezone stage on each time step to create mesh which satisfies equi-distribution principle for monitor function. The number of generators was chosen to guarantee required spatial resolution where the modified monitor reaches its maximum value. We present all details required for implementation of new adaptive ReALE methods and demonstrate their performance in comparison with standard ReALE method on series of numerical examples.