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

Abstract

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.

Experimental and Numerical Investigation of Ice Crystal Icing on a Heatable NACA0012 Airfoil

“…To do this, a coupling procedure derived from [13] is used. To close the coupling, a relationship is needed between + 0 and the corresponding average temperature of the ice layer which is the only available information on the temperature profile in the accretion shape, since Eqs.…”

Numerical Simulation of an Electrothermal Ice Protection System in Anti-Icing and Deicing Mode

“…They are chosen to minimize the number of sub-iterations required to reach convergence. More details may be found in [23].…”

“…This method is implemented in the icing suite described in Figure 3. The coupling between the ice accretion solver and the heat conduction solver modelling the protection system is performed using a Schwarz approach as described in [23].…”

“…IGLOO2D's unsteady ice accretion solver and heat conduction solver and their coupling was presented in previous work [22,23]. However, the methodology was presented from a numerical standpoint.…”

Ice crystals accretion capabilities of ONERA’s 3D icing suite

“…Hence a specific coupling algorithm must be implemented to obtain a converged solution. Different coupling algorithms exist and have been successfully implemented in other solvers such as ONERA-IGLOO2D (see [16][17][18]). For a conduction problem, three different interface conditions can be used: Dirichlet, Neumann or Fourier-Robin.…”