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

Abstract : Within 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.
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https://hal.archives-ouvertes.fr/hal-00828629
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Julien Bruchon, Sylvain Drapier, François Valdivieso. 3D finite element simulation of the matter flow by surface diffusion using a level set method. International Journal for Numerical Methods in Engineering, Wiley, 2011, 86 (7), pp.845-861. ⟨10.1002/nme.3079⟩. ⟨hal-00828629⟩

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