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 targeted 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.

在模拟复杂的物理现象（例如飞机除冰或除冰）时，经常需要将几个专用的求解器强耦合。在这项工作中，以非稳定的除冰仿真为目标应用，构建了一种不重叠的Schwarz方法。为此，首先针对具有线性边界条件的一维非稳态热方程和具有非线性边界条件的稳态热方程推导最佳耦合系数。显示了这些系数的选择以保证该方法的收敛性。然后使用边界条件的线性化，将该方法扩展到一般的不稳定热传导问题的情况。在简单情况下对该方法进行了测试，并从理论和数值上评估了收敛性。