scholarly journals Reply to comment on “On the continuum-scale modeling of gravity-driven fingers in unsaturated porous media: The inadequacy of the Richards equation with standard monotonic constitutive relations and hysteretic equations of state” by Mehdi Eliassi and Robe

2003 ◽  
Vol 39 (9) ◽  
Author(s):  
M. Eliassi ◽  
R. J. Glass
Keyword(s):  
Porous Media ◽  
Equations Of State ◽  
Constitutive Relations ◽  
Richards Equation ◽  
Unsaturated Porous Media ◽  
Scale Modeling ◽  
Gravity Driven ◽  
Continuum Scale ◽  
The Continuum

Global random walk solvers for fully coupled flow and transport in saturated/unsaturated porous media

2021 ◽  
Author(s):  
Nicolae Suciu ◽  
Davide Illiano ◽  
Alexander Prechtel ◽  
Florin Radu
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Random Walk ◽  
Transport Processes ◽  
Richards Equation ◽  
Unsaturated Porous Media ◽  
Coupled Flow ◽  
Flow And Transport ◽  
Coupled Flow And Transport ◽  
Fully Coupled

<p>We present new random walk methods to solve flow and transport problems in saturated/unsaturated porous media, including coupled flow and transport processes in soils, heterogeneous systems modeled through random hydraulic conductivity and recharge fields, processes at the field and regional scales. The numerical schemes are based on global random walk algorithms (GRW) which approximate the solution by moving large numbers of computational particles on regular lattices according to specific random walk rules. To cope with the nonlinearity and the degeneracy of the Richards equation and of the coupled system, we implemented the GRW algorithms by employing linearization techniques similar to the <em>L</em>-scheme developed in finite element/volume approaches. The resulting GRW <em>L</em>-schemes converge with the number of iterations and provide numerical solutions that are first-order accurate in time and second-order in space. A remarkable property of the flow and transport GRW solutions is that they are practically free of numerical diffusion. The GRW solvers are validated by comparisons with mixed finite element and finite volume solvers in one- and two-dimensional benchmark problems. They include Richards' equation fully coupled with the advection-diffusion-reaction equation and capture the transition from unsaturated to saturated flow regimes.  For completeness, we also consider decoupled flow and transport model problems for saturated aquifers.</p>

scholarly journals Global existence of weak solutions to unsaturated poroelasticity

2021 ◽  
Author(s):  
Jakub Both ◽  
Iuliu Sorin Pop ◽  
Ivan Yotov
Keyword(s):  
Porous Media ◽  
Weak Solutions ◽  
Constitutive Relations ◽  
Richards Equation ◽  
Existence Of Weak Solutions ◽  
Continuity Properties ◽  
Consolidation Model ◽  
Multi Phase Flow ◽  
Multi Phase ◽  
Compactness Arguments

We study unsaturated poroelasticity, i.e., coupled hydro-mechanical processes in variably saturated porous media, here modeled by a non-linear extension of Biot's well-known quasi-static consolidation model. The coupled elliptic-parabolic system of partial differential equations is a simplified version of the general model for multi-phase flow in deformable porous media, obtained under similar assumptions as usually considered for Richards' equation. In this work, existence of weak solutions is established in several steps involving a numerical approximation of the problem using a physically-motivated regularization and a finite element/finite volume discretization. Eventually, solvability of the original problem is proved by a combination of the Rothe and Galerkin methods, and further compactness arguments. This approach in particular provides the convergence of the numerical discretization to a regularized model for unsaturated poroelasticity. The final existence result holds under non-degeneracy conditions and natural continuity properties for the constitutive relations. The assumptions are demonstrated to be reasonable in view of geotechnical applications.

Sign in / Sign up

Export Citation Format

Share Document