A linear domain decomposition method for partially saturated flow in porous media

The Richards equation is a nonlinear parabolic equation that is commonly used for modelling saturated/unsaturated flow in porous media. We assume that the medium occupies a bounded Lipschitz domain partitioned into two disjoint subdomains separated by a fixed interface $\Gamma$. This leads to two problems defined on the subdomains which are coupled through conditions expressing flux and pressure continuity at $\Gamma$. After an Euler implicit discretisation of the resulting nonlinear subproblems a linear iterative ($L$-type) domain decomposition scheme is proposed. The convergence of the scheme is proved rigorously. In the last part we present numerical results that are in line with the theoretical finding, in particular the unconditional convergence of the scheme. We further compare the scheme to other approaches not making use of a domain decomposition. Namely, we compare to a Newton and a Picard scheme. We show that the proposed scheme is more stable than the Newton scheme while remaining comparable in computational time, even if no parallelisation is being adopted. Finally we present a parametric study that can be used to optimize the proposed scheme.Comment: 34 pages, 13 figures, 7 table

Towards hybrid two-phase modelling using linear domain decomposition

The viscous flow of two immiscible fluids in a porous medium on the Darcy scale is governed by a system of nonlinear parabolic equations. If infinite mobility of one phase can be assumed (e.g., in soil layers in contact with the atmosphere) the system can be substituted by the scalar Richards model. Thus, the porous medium domain may be partitioned into disjoint subdomains where either the full two-phase or the simplified Richards model dynamics are valid. Extending the previously considered one-model situations we suggest coupling conditions for this hybrid model approach. Based on an Euler implicit discretization, a linear iterative (L-type) domain decomposition scheme is proposed, and proved to be convergent. The theoretical findings are verified by a comparative numerical study that in particular confirms the efficiency of the hybrid ansatz as compared to full two-phase model computations.publishedVersio

A linear domain decomposition method for partially saturated flow in porous media

\u3cp\u3eThe Richards equation is a nonlinear parabolic equation that is commonly used for modelling saturated/unsaturated flow in porous media. We assume that the medium occupies a bounded Lipschitz domain partitioned into two disjoint subdomains separated by a fixed interface Γ. This leads to two problems defined on the subdomains which are coupled through conditions expressing flux and pressure continuity at Γ. After an Euler implicit discretisation of the resulting nonlinear subproblems, a linear iterative (L-type) domain decomposition scheme is proposed. The convergence of the scheme is proved rigorously. In the last part we present numerical results that are in line with the theoretical finding, in particular the convergence of the scheme under mild restrictions on the time step size. We further compare the scheme to other approaches not making use of a domain decomposition. Namely, we compare to a Newton and a Picard scheme. We show that the proposed scheme is more stable than the Newton scheme while remaining comparable in computational time, even if no parallelisation is being adopted. After presenting a parametric study that can be used to optimise the proposed scheme, we briefly discuss the effect of parallelisation and give an example of a four-domain implementation.\u3c/p\u3

Approches pratiques de l'enseignement des langues de spécialité

Source de motivation, le centrage des cours de langue sur la spécialité des apprenants s’avère être l’une des démarches capables de réconcilier des groupes d’étudiants en situation de blocage et de niveau très hétérogène avec la langue. L’idée a fait son chemin et de nombreuses méthodes sont maintenant utilisées : enseignement par les tâches (thème du Congrès de l’APLIUT cette année), enseignement par objectifs, classes de langues intégrées, expériences sur le terrain (stages), jeux d’entreprise, projets tuteurés, études de cas, etc. Les articles et fiches pédagogiques que nous vous proposons dans ce volume des Cahiers de l’APLIUT explorent certaines de ces pistes et insistent sur la nécessité de donner une orientation professionnelle à l’enseignement des langues de spécialité. Nous publions ici quatre articles, trois fiches pédagogiques et deux recensions d’ouvrages. Le premier article s’adresse essentiellement aux enseignants qui ont à créer un cours de langue de spécialité ; le deuxième traite des stages à l’étranger ; les deux autres articles ainsi que les trois fiches pédagogiques présentent d’autres approches pratiques de l’enseignement