Advection approaches for single- and multi-material arbitrary Lagrangian–Eulerian finite element procedures

Abstract

The essential feature in arbitrary Lagrangian-Eulerian (ALE) based finite element approaches is the additional requirement to consider flow effects of the materials and the solution variables through the computational domain. These flow effects are commonly known as advective effects. The present paper examines different advection strategies for the application of the ALE finite element method in a finite deformation solid mechanics framework, where especially micromechanical problems are referred to. The global solution algorithm is based on the well-known fractional step method that provides an operator splitting approach for the solution of the coupled ALE equations. Distinguishing the so-called single-material and the multi-material ALE method, different advection schemes based on volume-and material-associated advection procedures are required. For the latter case, the material interfaces are not resolved explicitly by the finite element mesh. Instead a volume-of-fluid interface tracking approach in terms of the volume fractions of the different material phases is applied.

Vibro-Injection Pile Installation in Sand: Part II—Numerical and Experimental Investigation

“…Modern nonlinear algorithms can avoid spurious oscillation and at the same time achieve a maximum accuracy of second or higher order in space. The state of the art in the field of MMALE are high-resolution nonlinear schemes, for example total variation diminishing (TVD) algorithms [11,24,27,35]. Such an algorithm will be also implemented into the developed MMALE method.…”

“…q def = f k q k . If one would simply use this definition in the general finite volume-based transport algorithm (13), however, the initially coherent material phases would disperse after a few advection steps because the interfacial structure is not accounted for [24].…”

An ALE method for penetration into sand utilizing optimization-based mesh motion

“…Finite volume methods have traditionally been pursued by the CFD community [38,39] and have earned broad recognition in the history of development of ALE and related methods [2,5,6,40,12,41]. They are conservative because they solve the integral form of the conservation law (4) 2 ,…”

“…The current method approximates this term by a weighted donor-cell (Godunov-type) flux function. Donor-cell advection is used in many ALE codes [2,6,40,12,41] because it has some highly desirable features [38,39].…”

Numerical techniques for rolling rubber wheels: treatment of inelastic material properties and frictional contact

“…A survey of different numerical advection schemes is given in [2,12]. Most of the numerical advection schemes suffer from problem dependent specific numerical inaccuracies like diffusive or dispersive effects as well as oscillatory response.…”