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.

在瞬态状态下移动源和移动内部边界的问题在许多研究领域和工程应用中都引起了人们的高度关注。正确解决此类问题的一种方法是基于非匹配网格的 Chimera 方法，其中每个移动对象都定义在穿过固定粗糙背景移动的精细网格上。通过这种方式，移动源或边界周围的高梯度被精细网格捕获，而无需全局精细固定网格或自适应细化。在这项工作中，Chimera 在有限元方法的框架中实现，遵循任意拉格朗日-欧拉公式用于移动网格和标准欧拉公式用于固定背景网格。此外，在对流为主的问题的情况下，该方案使用流线逆风彼得罗夫-加勒金方法稳定。移动细网格和粗固定网格之间的耦合是通过 Dirichlet 边界条件和高阶插值算法实现的。所提出的方法在准确性和稳定性方面的性能通过数值测试来评估，以与使用固定网格解决的等效问题进行比较。进一步的测试有助于突出所提出的基于 Chimera 的有限元方法的良好性能，以解决具有多个移动边界和源的对流主导问题以及三维弧焊工艺。所提出的方法在准确性和稳定性方面的性能通过数值测试来评估，以与使用固定网格解决的等效问题进行比较。进一步的测试有助于突出所提出的基于 Chimera 的有限元方法的良好性能，以解决具有多个移动边界和源的对流主导问题以及三维弧焊工艺。所提出的方法在准确性和稳定性方面的性能通过数值测试来评估，以与使用固定网格解决的等效问题进行比较。进一步的测试有助于突出所提出的基于 Chimera 的有限元方法的良好性能，以解决具有多个移动边界和源的对流主导问题以及三维弧焊工艺。