A non-overlapping optimized Schwarz method for the heat equation with non linear boundary conditions and with applications to de-icing

Lokman Bennani (1) , Pierre Trontin (1) , Rémi Chauvin (2) , Philippe Villedieu (1)

1 DMPE, ONERA, Université de Toulouse [Toulouse]
2 LDG - Laboratoire de Détection et de Géophysique (CEA)

When simulating complex physical phenomena such as aircraft icing or de-icing, several dedicated solvers often need to be strongly coupled. In this work, a non-overlapping Schwarz method is constructed with the unsteady simulation of de-icing as the targetted application. To do so, optimized coupling coefficients are first derived for the one dimensional unsteady heat equation with linear boundary conditions and for the steady heat equation with non-linear boundary conditions. The choice of these coefficients is shown to guarantee the convergence of the method. Using a linearization of the boundary conditions, the method is then extended to the case of a general unsteady heat conduction problem. The method is tested on simple cases and the convergence properties are assessed theoretically and numerically. Finally the method is applied to the simulation of an aircraft electrothermal de-icing problem in two dimensions.

Mots clés: NUMERICAL SIMULATION; SCHWARZ METHOD; COUPLING; AIRCRAFT ICING; ELECTROTHERMAL DE-ICING

Mots clés: SIMULATION NUMERIQUE; METHOD SCHWARZ; COUPLAGE; GIVRAGE AVION; DEGIVRAGE ELECTROTHERMIQUE

Domaines: Sciences de l'ingénieur [physics]; Physique [physics]

Lokman Bennani, Pierre Trontin, Rémi Chauvin, Philippe Villedieu. A non-overlapping optimized Schwarz method for the heat equation with non linear boundary conditions and with applications to de-icing. Computers & Mathematics with Applications, 2020, 80 (6), pp.1500-1522. ⟨10.1016/j.camwa.2020.07.017⟩. ⟨hal-02969163⟩