Arrarás Ventura, AndrésPortero Egea, LauraJorge Ulecia, Juan Carlos2023-09-112023-09-112007Arrarás, A., Portero, L., & Jorge, J. C. (2008). Parallel solution of nonlinear parabolic problems on logically rectangular grids. En R. Wyrzykowski, J. Dongarra, K. Karczewski, & J. Wasniewski (Eds.), Parallel Processing and Applied Mathematics (Vol. 4967, pp. 371-380). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-68111-3_39978-3-540-68105-210.1007/978-3-540-68111-3_39https://academica-e.unavarra.es/handle/2454/46306This work deals with the efficient numerical solution of nonlinear transient flow problems posed on two-dimensional porous media of general geometry. We first consider a spatial semidiscretization of such problems by using a cell-centered finite difference scheme on a logically rectangular grid. The resulting nonlinear stiff initial-value problems are then integrated in time by means of a fractional step method, combined with a decomposition of the flow domain into a set of overlapping subdomains and a linearization procedure which involves suitable Taylor expansions. The proposed algorithm reduces the original problem to the solution of several linear systems per time step. Moreover, each one of such systems can be directly decomposed into a set of uncoupled linear subsystems which can be solved in parallel. A numerical example illustrates the unconditionally convergent behaviour of the method in the last section of the paper.application/pdfeng© 2008 Springer-Verlag Berlin HeidelbergDomain decompositionFractional step methodLinearly implicit methodLogically rectangular gridNonlinear parabolic problemSupport-operator methodinfo:eu-repo/semantics/conferenceObject2023-09-11info:eu-repo/semantics/openAccess