A truly mesh-distortion-enabled implementation of cell-based smoothed finite element method for incompressible fluid flows with fixed and moving boundaries

Mesh-free properties are part of the superiority of cell-based smoothed finite element method (CS-FEM), but have yet to be fully exploited for computational fluid dynamics. A novel implementation of CS-FEM for incompressible viscous fluid flows in stationary and deforming domains discretized by severely distorted bilinear four-node quadrilateral (Q4) elements is presented in this article. The negative determinant of the Jacobian transformation from the Cartesian coordinates to the natural coordinates is intentionally stipulated for the corresponding mesh over which FEM inevitably fails in practice. It is found that, without ad hoc modifications, CS-FEM incurs unsatisfactory results and even a failure on fixed meshes. To cater for general computations on either a uniform or nonuniform mesh represented by these badly degenerated elements, four smoothing cells (SCs) are deployed in convex Q4 element whereas one SC in concave Q4 element. A simple hourglass control is introduced into those under-integrated quadrilaterals for stabilizing the one-SC quadrature in smoothed Galerkin weak form. Thanks to the adoption of characteristic-based split (CBS) scheme for the fluid solution, a byproduct is the unfolded equivalence of the CBS stabilization and balancing tensor diffusivity under the incompressibility constraint. Several benchmark problems involving incompressible fluid flow and fluid-structure interaction are solved. Numerical results show the good accuracy and robustness of the proposed approach that raises a seductive idea for resolving moving-mesh problems.