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ENCIT 2020
18th Brazilian Congress of Thermal Sciences and Engineering
A Two-Dimensional Element-Based Finite Volume Method for Solving the Poroelastic Problem
Submission Author:
Gustavo Ribeiro , SC , Brazil
Co-Authors:
Gustavo Ribeiro, Fernando Sandro Velasco Hurtado, Clovis Maliska
Presenter: Gustavo Ribeiro
doi://10.26678/ABCM.ENCIT2020.CIT20-0165
Abstract
The present work considers the Biot’s theory of consolidation for deriving a numerical model for solving coupled fluid flow and geomechanics problems in porous media. Normally these equations are solved using different numerical tools, being the most common approach the use of the finite element method for the geomechanical problem and the finite volume method for the fluid flow problem. The use of finite element for the rock mechanics is mainly a tradition of using this method for solid mechanics. In this work, on the other hand, both problems are solved using a finite volume technique, the Element-based Finite Volume Method (EbFVM), in the framework of the same two-dimensional unstructured grid. The coupled system of discretized equations is solved in an iterative way, in which the equation of each model are solved separately, exchanging information at all time steps. Two classic problems with known analytical solutions are solved to validate the proposed numerical approach, the Terzaghi’s poroelastic column and Mandel's problem. In both cases the obtained numerical solutions are very close to the analytical ones, showing that the presented methodology is very promising for solving coupled problems.
Keywords
geomechanics, poroelastic problem, Finite volume method, unstructured grids, coupled solution
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