Analysis of a full discretization scheme for a 2D nonlinear coupled system of radiative-conductive heat transfer equations

Mohamed Ghattassi (1) , Jean-Rodolphe Roche (2) , Didier Schmitt (2)

1 KAUST - King Abdullah University of Science and Technology [Saudi Arabia]
2 IECL - Institut Élie Cartan de Lorraine

This paper deals with the convergence of numerical scheme for combined nonlinear radiation–conduction heat transfer system in a gray, absorbing and non-scattering two-dimensional medium. The radiative transfer equation is solved using a Discontinuous Galerkin method with upwind fluxes. The conductive equation is discretized using the finite element method. Moreover, the Crank–Nicolson scheme is applied for time discretization of the semi-discrete nonlinear coupled system. Existence and uniqueness of the solution for the continuous and full discrete system are presented. The convergence proof follows from the application of a discrete fixed-point theorem, involving only the temperature fields at each time step. The order of approximation error, stability, and order of convergence are investigated. Finally, the theoretical stability and convergence results are supported with numerical examples

Mots clés: Galerkin method; Crank-Nicolson scheme; Radiative-conductive heat transfer; error estimates; Banach fixed point theorem

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Mohamed Ghattassi, Jean-Rodolphe Roche, Didier Schmitt. Analysis of a full discretization scheme for a 2D nonlinear coupled system of radiative-conductive heat transfer equations. Journal of Computational and Applied Mathematics, 2019, 346, pp.1-17. ⟨10.1016/j.cam.2018.06.028⟩. ⟨hal-01283667v2⟩