A cell-based smoothed finite element method for three-dimensional laminar flow and convective heat transfer on mixed meshes

作者：Chen Hong, Chen Jiang, Jingyu Wang, Yichao Qiu, Guo Zhou · 发表于：Physics of Fluids · 年份：2026 · DOI：10.1063/5.0342015 · 研究领域：Advanced Numerical Methods in Computational Mathematics、Computational Fluid Dynamics and Aerodynamics、Lattice Boltzmann Simulation Studies

The smoothed finite element method has demonstrated substantial potential in computational fluid dynamics, but its application to three-dimensional (3D) convective heat transfer remains limited, particularly for coupled flow and thermal transport on mixed meshes. In this work, the cell-based smoothed finite element method (CS-FEM) is extended to 3D incompressible laminar flow with convective heat transfer. A characteristic-based split scheme is incorporated into a fractional-step framework to improve numerical stability and suppress pressure oscillations. The proposed method is first assessed using a manufactured solution on tetrahedral, wedge, and hexahedral meshes, demonstrating accuracy and convergence across different element topologies. It is then validated using 3D natural convection in a side-heated cubic cavity, where comparisons with benchmark data and a strongly distorted mesh test confirm its accuracy and robustness. Transient forced convection past a sphere is further considered to evaluate the method under unsteady thermo-fluid conditions. Finally, CS-FEM on a mixed mesh is applied to laminar flow and heat transfer in a Gyroid-type triply periodic minimal surface (TPMS) structure. The predicted flow and thermal fields agree closely with those obtained using a commercial finite volume solver, with smooth velocity and temperature profiles near highly curved walls in the unstructured mesh regions. The Gyroid TPMS application demonstrates the method's capability to r...