Some improvements on free surface simulation by the particle finite element method

Abstract

SUMMARYThe Lagrangian method has become increasingly popular in numerical simulation of free surface problems. In this paper, after a brief review of a recent Lagrangian method, namely the particle finite element method, some issues are discussed and some improvements are made. The least-square finite element method is adopted to simplify the solving of the Navier-Stokes equations. An adaptive time method is derived to obtain suitable time steps. A mass correction procedure is imported to improve the mass conservation in long time calculations and time discretization scheme is adopted to decrease the pressure oscillations during the calculations.Finally, the method is used to simulate a series of examples and the results are compared with the commercial FLOW3D code.

Lagrangian formulation for finite element analysis of quasi‐incompressible fluids with reduced mass losses

“…Application of the PFEM in fluid and solid mechanics and in fluid-structure interaction problems can be found in [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], as well in www.cimne.com/pfem. Application of the PFEM in fluid and solid mechanics and in fluid-structure interaction problems can be found in [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], as well in www.cimne.com/pfem.…”

“…Our interest in this work is the modeling and simulation of free surface quasi-incompressible flows accounting for the actual value of the speed of sound in the fluid (or the equivalent bulk modulus) using a particular class of Lagrangian FEM termed the particle FEM (PFEM, www.cimne.com/pfem) [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. The PFEM treats the mesh nodes in the fluid and solid domains…”

On the effect of standard PFEM remeshing on volume conservation in free-surface fluid flow problems

“…The Particle Finite Element Method (PFEM) is a numerical strategy specifically designed for those problems where severe changes of topology occur, such as free surface fluid dynamics [22,25,10,42,8], granular flows [43,4], non-linear solid mechanics [6], Fluid-Structure Interaction (FSI) [16,19,44,40], or thermal coupled problems [1,30,37].…”

Unified Lagrangian Formulation for Fluid and Solid Mechanics, Fluid-Structure Interaction and Coupled Thermal Problems Using the PFEM

“…In the last years, many scientific publications have shown the efficacy of the PFEM for solving free surface flow problems, see among others [32,68,117]. The PFEM has also been tested successfully in other kind of problems, such as fluid mechanics including thermal convection-diffusion [5,80,95], multi-fluids [36,62], granular materials [131], bed erosion [87], FSI [81,132] and excavation [19].…”