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Numerical simulations for predicting the microstructural evolution of ferritic alloys. A study of Cluster Dynamics.

Pierre Terrier 1, 2
CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique, Inria de Paris
Abstract : We study ageing of materials at a microstructural level. In particular, defects such as vacancies, interstitials and solute atoms are described by a model called Cluster Dynamics (CD), which characterize the evolution of the concentrations of such defects, on period of times as long as decades. CD is a set of ordinary differential equations (ODEs), which might contain up to hundred of billions of equations. Therefore, classical methods used for solving system of ODEs are not suited in term of efficiency. We first show that CD is well-posed and that physical properties such as the conservation of matter and the preservation of the sign of the solution are verified. We also study an approximation of CD, namely the Fokker–Planck approximation, which is a partial differential equation. We quantify the error between CD and its approximation. We then introduce an algorithm for simulating CD. The algorithm is based on a splitting of the dynamics and couples a deterministic and a stochastic approach of CD. The stochastic approach interprets directly CD as a jump process or its approximation as a Langevin process. The aim is to reduce the number of equations to solve, hence reducing the computation time. We finally apply this algorithm to physical models. The interest of this approach is validated on complex models. Moreover, we show that CD can be efficiently improved thanks to the versatility of the algorithm.
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Submitted on : Wednesday, January 23, 2019 - 11:12:37 AM
Last modification on : Monday, April 8, 2019 - 6:07:33 PM


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Pierre Terrier. Numerical simulations for predicting the microstructural evolution of ferritic alloys. A study of Cluster Dynamics.. Analysis of PDEs [math.AP]. Université Paris-Est, 2018. English. ⟨tel-01990556⟩



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