Portero Egea, Laura

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https://academica-e.unavarra.es/handle/2454/49803

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Portero Egea

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Laura

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Estadística, Informática y Matemáticas

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InaMat2. Instituto de Investigación en Materiales Avanzados y Matemáticas

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0000-0002-7521-2097

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88600

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2608

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Subject: Fractional step method ×

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    PublicationOpen Access
    Parallel solution of nonlinear parabolic problems on logically rectangular grids
    (Springer, 2007) Arrarás Ventura, Andrés; Portero Egea, Laura; Jorge Ulecia, Juan Carlos; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
    This 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.