Mesh deformation and adaptive refinement for physical fields

Physical field simulations demand efficient mesh deformation and adaptive refinement methods. This paper proposes a systematical method tailored to the specific needs of simulations. Interpolation-based methods are preferred for large-scale mesh deformation due to computational efficiency. Improving the inverse distance weighted method by introducing auxiliary nodes using the sub-mesh. A node smoothing algorithm based on layered mesh is also devised to enhance mesh deformation ability. Optimizing the convergence criterion greatly reduces computation time.

To improve element quality after deformation and meet the requirement for iterative refinement of mesh in simulation, a mesh refinement method is proposed. To address challenges in inserting nodes into narrow spaces, a novel algorithm is developed, which integrates the boundary constraints with the longest-edge propagation path. The co-optimization of surface and tetrahedral meshes is achieved through an algorithm based on size-field and an improved surface priority insertion strategy. A boundary edge priority algorithm is proposed to preserve the fitness between mesh and geometry. Flow field examples demonstrate the method’s effectiveness in mesh deformation and the optimization of poor-quality elements. Electromagnetic simulation results show that, compared to commercial software, the method significantly reduces the number of elements after refinement while maintaining solver accuracy.