A novel Lagrangian finite element method with adaptive element-particle conversion ability for incompressible flows with free surfaces

Abstract

When modeling fluid flows with the finite element method (FEM), a normal way is to implement the simulation in an Eulerian frame, as it is difficult for the Lagrangian FEM to deal with fluid flows with extremely large deformations, especially for incompressible flows with violent fluid-structure interactions along with changing free surfaces. In this paper, we developed a novel Lagrangian FEM for modeling incompressible flows with violently changing free surfaces. The Lagrangian FEM is an edge-based smoothed FEM (ES-FEM) which has special advantages over the conventional FEM due to the gradient smoothing technique. An artificial equation of state is used in the ES-FEM to treat the incompressible flow as weakly compressible. In order to simulate large fluid deformation, an adaptive algorithm is employed to convert the FEM elements in areas with large fluid deformation into particles in the smoothed particle hydrodynamics (SPH) as the SPH method is well suited for modeling fluid deformation and free surfaces. Some state-of-art algorithms including the kernel gradient correction and particle shift technique are integrated into the SPH method to ensure the computational accuracy of the fluid modeling. After such treatment, the Lagrangian ES-FEM is used for modeling fluid flows with small deformations while SPH is employed for areas with large fluid deformations where ES-FEM elements are automatically converted to SPH particles. Four numerical examples including still water, lid driven cavity flow, dam break and water entry are modeled using the present Lagrangian FEM. The numerical studies demonstrate that the present Lagrangian FEM with adaptive element-particle conversion ability is as accurate as SPH in modeling incompressible flows with violently changing free surfaces while it is much more efficient than SPH.