CI²MA - Publications | Preprints

Preprint 2018-32

Sarvesh Kumar, Ricardo Oyarzua, Ricardo Ruiz-Baier, Ruchi Sandilya:

Conservative discontinuous fi nite volume and mixed schemes for a new four-fi eld formulation in poroelasticity

Abstract:

We introduce a hybrid numerical method for the approximation of linear poroelasticity equations, representing the interaction between the non-viscous fi ltration flow of a fluid and the linear me- chanical 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 fi nite 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. The resulting discrete problems exhibit a double saddle-point structure, and their solvability and stability are established in terms of bounds that do not depend on the modulus of dilation of the solid. We derive optimal error estimates in suitable norms, for all eld variables; and we exemplify the convergence and locking-free properties of this scheme through a series of numerical tests.

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