Domain decomposition methods for the numerical resolution of the aluminium casting process

Nonoverlapping domain decomposition methods are very adequated to solve problems involving PDE in nonhomogeneous domains. In the case of the aluminium casting process these techniques are needed if the problem is to be formulated in enthalpy, due to the lack of continuity of the Kirchoff variable on the boundary between physical subdomains, the aluminium and the mold. In this paper a family of domain decomposition methods based on the numerical approximation of the Euler equations associated to a saddle point of different Lagrangian functionals are obtained. The main difference amongst these methods is the way in which interface conditions between subdomains are established. The convergence properties of these methods have been experimentally studied for a linear case, and the numerical results obtained for the industrial problem of aluminium solidification in a cast are finally presented.