scholarly journals Preconditioning Techniques for the Numerical Solution of Flow in Fractured Porous Media

2020 ◽  
Vol 86 (1) ◽  
Author(s):  
Paola F. Antonietti ◽  
Jacopo De Ponti ◽  
Luca Formaggia ◽  
Anna Scotti
Keyword(s):  
Porous Media ◽  
Three Dimensional ◽  
Iterative Solution ◽  
Fractured Porous Media ◽  
Iterative Solvers ◽  
Preconditioning Techniques ◽  
Darcy Problem ◽  
Finite Difference Discretization ◽  
Block Factorization ◽  
Discrete Formulation

AbstractThis work deals with the efficient iterative solution of the system of equations stemming from mimetic finite difference discretization of a hybrid-dimensional mixed Darcy problem modeling flow in fractured porous media. We investigate the spectral properties of a mixed discrete formulation based on mimetic finite differences for flow in the bulk matrix and finite volumes for the fractures, and present an approximation of the factors in a set of approximate block factorization preconditioners that accelerates convergence of iterative solvers applied to the resulting discrete system. Numerical tests on significant three-dimensional cases have assessed the properties of the proposed preconditioners.

scholarly journals Thermal convection in three-dimensional fractured porous media

2018 ◽  
Vol 97 (1) ◽  
Author(s):  
C. Mezon ◽  
V. V. Mourzenko ◽  
J.-F. Thovert ◽  
R. Antoine ◽  
F. Fontaine ◽  
...  
Keyword(s):  
Porous Media ◽  
Thermal Convection ◽  
Three Dimensional ◽  
Fractured Porous Media

scholarly journals Dual Virtual Element Methods for Discrete Fracture Matrix models

2019 ◽  
Vol 74 ◽  
pp. 41 ◽  
Author(s):  
Alessio Fumagalli ◽  
Eirik Keilegavlen
Keyword(s):  
Porous Media ◽  
Computational Cost ◽  
Three Dimensional ◽  
Simulation Models ◽  
Passive Scalar ◽  
High Ratio ◽  
Fractured Porous Media ◽  
Computational Grids ◽  
Geothermal System ◽  
Darcy Velocity

The accurate description of fluid flow and transport in fractured porous media is of paramount importance to capture the macroscopic behavior of an oil reservoir, a geothermal system, or a CO2 sequestration site, to name few applications. The construction of accurate simulation models for flow in fractures is challenging due to the high ratio between a fracture’s length and width. In this paper, we present a mixed-dimensional Darcy problem which can represent the pressure and Darcy velocity in all the dimensions, i.e. in the rock matrix, in the fractures, and in their intersections. Moreover, we present a mixed-dimensional transport problem which, given the Darcy velocity, describes advection of a passive scalar into the fractured porous media. The approach can handle both conducting and blocking fractures. Our computational grids are created by coarsening of simplex tessellations that conform to the fracture’s surfaces. A suitable choice of the discrete approximation of the previous model, by virtual finite element and finite volume methods, allows us to simulate complex problems with a good balance of accuracy and computational cost. We illustrate the performance of our method by comparing to benchmark studies for two-dimensional fractured porous media, as well as a complex three-dimensional fracture geometry.

scholarly journals Verification benchmarks for single-phase flow in three-dimensional fractured porous media

2021 ◽  
Vol 147 ◽  
pp. 103759 ◽  
Author(s):  
Inga Berre ◽  
Wietse M. Boon ◽  
Bernd Flemisch ◽  
Alessio Fumagalli ◽  
Dennis Gläser ◽  
...  
Keyword(s):  
Porous Media ◽  
Single Phase ◽  
Three Dimensional ◽  
Fractured Porous Media ◽  
Phase Flow ◽  
Single Phase Flow
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