An efficient runtime mesh smoothing technique for 3D explicit Lagrangian free-surface fluid flow simulations

A fast runtime mesh smoothing algorithm for explicit Lagrangian simulations of 3D weakly compressible viscous fluid flows, implemented in conjunction with the particle finite element method (PFEM), is proposed. The formulation for weakly compressible fluids allows for the use of an explicit time integration scheme. Explicit solvers are appealing for large-scale engineering problems characterized by fast dynamics and/or a high degree of nonlinearity. However, the conditional stability of these schemes requires the use of small time increments, proportional to the size of the element in the mesh with the worst geometrical quality. The Lagrangian description of the PFEM requires an efficient and robust runtime mesh generator algorithm, such as the Delaunay tessellation, to create new meshes during the analysis, whenever the current ones get too distorted because of the motion of the mesh nodes. When 3D problems are considered, a computationally effective mesh-improving algorithm is also required because, in 3D, the Delaunay tessellation loses some of its optimality properties holding in 2D so that badly shaped tetrahedra are frequently included in the triangulation, leading to unacceptably small stable time step sizes for the explicit solver. To this purpose, a novel and efficient mesh smoothing technique is here proposed, exploiting an elastic analogy that allows for the use of the same explicit and parallelizable architecture of the fluid solver. This smoothing algorithm has been specifically designed to ensure reasonably large critical time step sizes at an acceptable computational cost. This is particularly appealing for the application of explicit Lagrangian PFEM in large-scale 3D engineering problems, but it could be conveniently applied also to regularize the mesh and improve the solution of implicit solvers.