A coupled electro-thermal Discontinuous Galerkin method

JOURNAL OF COMPUTATIONAL PHYSICS

卷:348

Article

Homsi, L.¹  Geuzaine, C.²  Noels, L.¹ 

[1] Univ Liege, Dept Aerosp & Mech Engn, CM3, Quartier Polytech 1,Allee Decouverte 9, B-4000 Liege, Belgium

[2] Univ Liege, Dept Elect Engn & Comp Sci, Quartier Polytech 1,Allee Decouverte 10, B-4000 Liege, Belgium

关键词: Discontinuous Galerkin method;    Electro-thermal coupling;    Nonlinear elliptic problem;    Error estimates;   

DOI  :  10.1016/j.jcp.2017.07.028

来源: Elsevier

【 摘 要 】

This paper presents a Discontinuous Galerkin scheme in order to solve the nonlinear elliptic partial differential equations of coupled electro-thermal problems. In this paper we discuss the fundamental equations for the transport of electricity and heat, in terms of macroscopic variables such as temperature and electric potential. A fully coupled nonlinear weak formulation for electro-thermal problems is developed based on continuum mechanics equations expressed in terms of energetically conjugated pair of fluxes and fields gradients. The weak form can thus be formulated as a Discontinuous Galerkin method. The existence and uniqueness of the weak form solution are proved. The numerical properties of the nonlinear elliptic problems i.e., consistency and stability, are demonstrated under specific conditions, i.e. use of high enough stabilization parameter and at least quadratic polynomial approximations. Moreover the prior error estimates in the H-1-norm and in the L-2-norm are shown to be optimal in the mesh size with the polynomial approximation degree. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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