3D finite element simulation of the matter flow by surface diffusion using a level set method

Abstract

SUMMARYWithin the context of the sintering process simulation, this paper proposes a numerical strategy for the direct simulation of the matter transport by surface diffusion, in two and three dimensions. The level set formulation of the surface diffusion problem is first established. The resulting equations are solved by using a finite element method. A stabilization technique is then introduced, in order to avoid the spurious oscillations of the grain boundary that are a consequence of the dependence of the surface velocity on the fourth-order derivative of the level set function. The convergence and the accuracy of this approach are proved by investigating the change in an elliptic interface under surface diffusion. Cases in direct relation with the sintering process are analyzed besides: sintering between two grains of the same size or of two different sizes. Finally, 3D simulations involving a small number of particles show the ability of the proposed strategy to deal with strong deformations of the grain surface (formation of necks) and to access directly important parameters such as the closed porosity rate.

Introduction to the level-set full field modeling of laths spheroidization phenomenon in α/β titanium alloys

“…The main idea is to solve the advection equation and to rebuild the metric properties of the level-set function in order to keep a distance function ‫,ݔ(߮∇‖(‬ ‫‖)ݐ‬ = 1) at least near the interface Γ(‫. )ݐ‬ Classical approaches consist in solving, separately, the convective part and the reinitialization part thanks to the resolution of a classical Hamilton-Jacobi system [11] or to adopt an unified advection and renormalization methodology by solving one single equation based on a smooth description of the level-set [15]. Here, a new approach is proposed.…”

“…Final time of all simulations is fixed to 1s. Table 1 summarizes all the parameters (time step, mesh size in the fine mesh zone, number of elements of the used mesh, method used), the CPU time of the simulations and the corresponding precision of the results obtained concerning the positions of (a(t),0) for ‫ݐ‬ ∈ ‫]ݏ1,0[‬ by using the unified convectiverenormalized approach described in [15] and the new one proposed here with different time step and h values. These cases are representatives of an important number of other performed simulations.…”

Introduction to the level-set full field modeling of laths spheroidization phenomenon in α/β titanium alloys

“…In all simulations ‫ܤ‬ is assumed to be homogeneous and equal to 1 ݉݉ ସ ‫.ݏ/‬ Exact velocity of the point (a(t),0) is known [15] and given by:…”

“…The methodology used to obtain the surface diffusion velocity is based on the finite element based strategy introduced by Bruchon et al in [4] [15].…”

Finite Element Simulation of Mass Transport During Sintering of a Granular Packing. Part I. Surface and Lattice Diffusions

“…Geometric properties of the surface (normal vector, curvature) can then be “easily” deduced from this level‐set function . The level‐set method is used in literature for simulating a large variety of phenomena involving moving interface, in particular surface diffusion problems, and mass transport by surface diffusion . The computation by finite element of the pressure inside the elastic grains is another difficult problem to address.…”