An efficient and high-fidelity local multi-mesh finite volume method for heat transfer and fluid flow problems in metal additive manufacturing

The multi-scale and nonlinear feature of additive manufacturing problems poses great challenges to numerical algorithms regarding computational efficiency and fidelity. In this work, we propose a novel local multi-mesh finite volume method for heat transfer and fluid flow problems in the additive manufacturing process. In this method, two sets of meshes (coarse base mesh and finer overlay mesh) are used to resolve the macroscopic temperature field of the whole domain and the mesoscopic heat transfer and fluid flow problem within a relatively small region covering the melt pool, respectively. The interaction between the base mesh and the overlay mesh is handled by the Dirichlet boundary conditions on the interface following the refinement-by-superposition idea, such that the powder-scale simulation is available with high efficiency. The finer mesh with cells of sub-powder size uses the arbitrary Lagrangian–Eulerian description and moves with the heat source to keep coverage of the region with high solution gradients. According to the moving feature of the finer mesh, a particle-volume fraction conversion scheme is introduced to update the material distribution. The local multi-mesh finite volume method is further combined with the discrete element method as well as a surface reconstruction method to alternatively solve the powder layering process and the laser melting process. A set of numerical cases is presented, and the numerical results are compared with analytical and experimental data from the literature, with good agreement in cases where such data is available. Moreover, the computational efficiency of the proposed method is proved to be dozens of times (16∼50 for the given size ratios of the melt pool to the whole domain) of the finite volume method using a uniform structured mesh. It is expected to be a powerful tool for efficiently achieving powder-scale simulation of the additive manufacturing process and other similar multi-scale problems.