An improved alternating direction implicit difference solution for 2D plane strain multiphase coupled steady-state diffusion equations

Two-dimensional multiphase coupling problems are ubiquitous in diverse research domains.However, when it comes to problems involving higher dimensions and multi-physics coupling, existing solutions struggle to provide even a preliminary prediction.This study proposes an improved alternating direction implicit (IADI) difference algorithm to solve these problems.A conventional difference mesh is first split and then reassembled into a new mesh that couples the individual phases.A virtual mesh is constructed on adjacent time layers, with the iteration between the virtual and real meshes carried out via matrix operations.The IADI solution has high computational efficiency and accuracy in a series of examples.