Artículos de Investigación

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    Item type:Publication,
    Rotation-Based Mixed Formulations for an Elasticity-Poroelasticity Interface Problem
    (2020)
    Verónica Anaya
    ;
    Zoa de Wijn
    ;
    Bryan Gómez-Vargas
    ;
    David Mora
    ;
    Ricardo Ruiz-Baier
    In this paper we introduce a new formulation for the stationary poroelasticity equations written using the rotation vector and the total fluid-solid pressure as additional unknowns, and we also write an extension to the elasticity-poroelasticity problem. The transmission conditions are imposed naturally in the weak formulation, and the analysis of the effective governing equations is conducted by an application of Fredholm's alternative. We also propose a monolithically coupled mixed finite element method for the numerical solution of the problem. Its convergence properties are rigorously derived and subsequently confirmed by a set of computational tests that include applications to subsurface flow in reservoirs as well as to dentistry-oriented problems.
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    Conservative discontinuous finite volume and mixed schemes for a new four-field formulation in poroelasticity
    (2020)
    Sarvesh Kumar
    ;
    Ricardo Oyarzúa
    ;
    Ricardo Ruiz-Baier
    ;
    Ruchi Sandilya
    <jats:p>We introduce a numerical method for the approximation of linear poroelasticity equations, representing the interaction between the non-viscous filtration flow of a fluid and the linear mechanical response of a porous medium. In the proposed formulation, the primary variables in the system are the solid displacement, the fluid pressure, the fluid flux, and the total pressure. A discontinuous finite volume method is designed for the approximation of solid displacement using a dual mesh, whereas a mixed approach is employed to approximate fluid flux and the two pressures. We focus on the stationary case and the resulting discrete problem exhibits a double saddle-point structure. Its solvability and stability are established in terms of bounds (and of norms) that do not depend on the modulus of dilation of the solid. We derive optimal error estimates in suitable norms, for all field variables; and we exemplify the convergence and locking-free properties of this scheme through a series of numerical tests.</jats:p>