On the performance of a Chimera-FEM implementation to treat moving heat sources and moving boundaries in time-dependent problems

Problems with moving sources and moving inner boundaries in transient regime are of high interest in many research fields and engineering applications. One approach to properly tackle such problems is based on the Chimera method for non-matching grids, where each moving object is defined on a fine mesh that moves across the fixed coarse background. In this way, the high gradients around moving sources or boundaries are captured by the fine mesh without need of globally fine fixed meshes or adaptive refinement. In this work, Chimera is implemented in the framework of the finite element method, following an arbitrary Lagrangian- Eulerian formulation for the moving meshes and a standard Eulerian formulation for the fixed background mesh. Further, in case of convection-dominated problems, the scheme is stabilized using the streamline upwind Petrov-Galerkin method. The coupling between the moving fine meshes and the coarse fixed one is achieved via Dirichlet boundary conditions and a high-order interpolation algorithm. The performance of the proposed methodology in terms of accuracy and stability is assessed by means of numerical tests to be compared with equivalent problems solved using fixed meshes. Further tests serve to highlight the good performance of the proposed Chimera-based finite element method to address both convection-dominated problems with multiple moving boundaries and sources, and three-dimensional arc welding processes.

Automated summary

Problems with moving sources and moving inner boundaries are effectively addressed using the Chimera method. The method is based on non-matching grids and captures high gradients by defining moving objects on fine meshes that move across fixed backgrounds. The Chimera method is implemented in the finite element method framework and is assessed for accuracy and stability through numerical tests, demonstrating its good performance in addressing convection-dominated problems and three-dimensional arc welding processes.