A cell-based smoothed finite element method for three-dimensional incompressible flows using Cartesian cut-cell meshes

Abstract

Cartesian cut-cell meshes are favored for their excellent complex geometric adaptability, orthogonality, and mesh generation convenience. However, the difficulty in constructing shape function for hanging-node and irregular cut-cell elements limits their use in a standard finite element method (FEM). Inspired by the point interpolation method shape function used in a smoothed finite element method (S-FEM) which adapts to the arbitrary shape of an element, this work proposes a cell-based S-FEM using Cartesian cut-cell meshes for incompressible flows. Four different types of cell-based smoothing domains (CSDs) are constructed and compared in the Cartesian cut-cell mesh, involving node-based CSD (NCSD), face-based CSD (FCSD), mixed CSD (MIXCSD), and tetrahedral CSD (T4CSD). The smoothed Galerkin weak form and semi-implicit characteristic-based split (CBS) scheme are employed for spatial discretization and stabilization of Naiver–Stokes (N–S) equations, respectively. Several numerical examples are utilized to compare the convergences, computational accuracy, and computational efficiency of proposed CSDs. The numerical results demonstrate that FCSD and T4CSD exhibit instability. Conversely, NCSD and MIXCSD exhibit good stability, and NCSD shows slightly higher computational accuracy than MIXCSD, but at a lower computational efficiency. Additionally, the results show that Cartesian cut-cell meshes offer superior computational accuracy compared to tetrahedral meshes. Therefore, the present method provides an attractive numerical technique for solving flow problems with complex geometries.