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

Abstract

Summary 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.

A State of the Art Review of the Particle Finite Element Method (PFEM)

“…Only recently, explicit time integration schemes have been used in PFEM formulations (see e.g. [17,72,73]. Explicit solvers are very appealing for fast dynamics problems and also for non-linear problems that may suffer from numerical issues of convergence.…”

“…This feature gives to mesh quality a crucial role for the computation efficiency of explicit methods because the presence of excessively distorted elements may lead to vanishing stable time step size and compromise the computation. For this reason [72] proposes an efficient mesh smoothing approach based on an elastic analogy to improve the worst elements, with a computational cost (12) ṗ + = compatible with the frequent remeshing procedure required by the PFEM.…”

PFEM–DEM for particle-laden flows with free surface

“…In particular, before the impact of the water against the vertical wall, it is possible to plot the advancing in time of the uid front and compare it to experimental and numerical results from the literature. Specically, the 3D numerical results taken as reference are from [28] and [30], where a Moving Particle Semi-implicit method (MPS) and an explicit PFEM were used, respectively. As in the above references, the following dimensionless variables are considered:…”

“…This is probably due to a not faithful modeling of the retaining wall removal. As pointed out in [30], in all the referenced numerical models the wall is removed instantaneously, while in the laboratory experience this process takes inevitably a nite time. For the same time interval considered in Figure 14, the time evolution of the positions of the six spherical particles is given in Figure 15 with the aim of allowing future comparisons with other CFD-DEM solvers.…”

“…Only the vertical and horizontal displacements are plotted since, during the considered time interval, the particles undergo a negligible traversal motion. [30] (explicit 3D PFEM). Experimental (EXP) results from Koshizuka et al [25], Hu et al [26] and M artin et al [24].…”