American Institute of Mathematical Sciences

Advanced
2007, 2007(Special): 794-803. doi: 10.3934/proc.2007.2007.794

Modelling of interfaces in unsaturated porous media

Mario Ohlberger 1, and  Ben Schweizer 2,

1. 

Mathematisches Institut, Universität Freiburg, Herrmann-Herder-Str. 10, D-79104 Freiburg, Germany
2. 

Mathematisches Institut, Universität Basel, Rheinsprung 21, CH-4051 Basel, Switzerland

Received  September 2006 Revised  July 2007 Published  September 2007

In this contribution we discuss interface conditions for unsaturated flow in porous media. Our aim is to provide a concise collection of the arguments that lead to the standard models for interfaces that either separate two porous media or a porous medium and void space. We furthermore present a regularization procedure for these interface conditions. In a singular limit, a nonlinear boundary condition of third kind can provide approximate solutions to the outflow condition of Signorini type.
Keywords: porous media, Richards equation, unsaturated °ow, interface conditions..
Mathematics Subject Classification: Primary: 76S05, 35K60, 35K6.
Citation: Mario Ohlberger, Ben Schweizer. Modelling of interfaces in unsaturated porous media. Conference Publications, 2007, 2007 (Special) : 794-803. doi: 10.3934/proc.2007.2007.794
[1]

S. Bonafede, G. R. Cirmi, A.F. Tedeev. Finite speed of propagation for the porous media equation with lower order terms. Discrete and Continuous Dynamical Systems, 2000, 6 (2) : 305-314. doi: 10.3934/dcds.2000.6.305
[2]

Eduard Marušić-Paloka, Igor Pažanin. Homogenization and singular perturbation in porous media. Communications on Pure and Applied Analysis, 2021, 20 (2) : 533-545. doi: 10.3934/cpaa.2020279
[3]

María Anguiano, Renata Bunoiu. Homogenization of Bingham flow in thin porous media. Networks and Heterogeneous Media, 2020, 15 (1) : 87-110. doi: 10.3934/nhm.2020004
[4]

Ioana Ciotir. Stochastic porous media equations with divergence Itô noise. Evolution Equations and Control Theory, 2020, 9 (2) : 375-398. doi: 10.3934/eect.2020010
[5]

Laurent Lévi, Julien Jimenez. Coupling of scalar conservation laws in stratified porous media. Conference Publications, 2007, 2007 (Special) : 644-654. doi: 10.3934/proc.2007.2007.644
[6]

Leda Bucciantini, Angiolo Farina, Antonio Fasano. Flows in porous media with erosion of the solid matrix. Networks and Heterogeneous Media, 2010, 5 (1) : 63-95. doi: 10.3934/nhm.2010.5.63
[7]

Cedric Galusinski, Mazen Saad. Water-gas flow in porous media. Conference Publications, 2005, 2005 (Special) : 307-316. doi: 10.3934/proc.2005.2005.307
[8]

Hugo Beirão da Veiga. A challenging open problem: The inviscid limit under slip-type boundary conditions.. Discrete and Continuous Dynamical Systems - S, 2010, 3 (2) : 231-236. doi: 10.3934/dcdss.2010.3.231
[9]

José M. Arrieta, Simone M. Bruschi. Very rapidly varying boundaries in equations with nonlinear boundary conditions. The case of a non uniformly Lipschitz deformation. Discrete and Continuous Dynamical Systems - B, 2010, 14 (2) : 327-351. doi: 10.3934/dcdsb.2010.14.327
[10]

Victor Ginting. An adjoint-based a posteriori analysis of numerical approximation of Richards equation. Electronic Research Archive, 2021, 29 (5) : 3405-3427. doi: 10.3934/era.2021045
[11]

Marco Berardi, Fabio V. Difonzo. A quadrature-based scheme for numerical solutions to Kirchhoff transformed Richards' equation. Journal of Computational Dynamics, 2022, 9 (2) : 69-84. doi: 10.3934/jcd.2022001
[12]

Thomas I. Seidman. Interface conditions for a singular reaction-diffusion system. Discrete and Continuous Dynamical Systems - S, 2009, 2 (3) : 631-643. doi: 10.3934/dcdss.2009.2.631
[13]

Youcef Amirat, Laurent Chupin, Rachid Touzani. Weak solutions to the equations of stationary magnetohydrodynamic flows in porous media. Communications on Pure and Applied Analysis, 2014, 13 (6) : 2445-2464. doi: 10.3934/cpaa.2014.13.2445
[14]

Cédric Galusinski, Mazen Saad. A nonlinear degenerate system modelling water-gas flows in porous media. Discrete and Continuous Dynamical Systems - B, 2008, 9 (2) : 281-308. doi: 10.3934/dcdsb.2008.9.281
[15]

Ting Zhang. The modeling error of well treatment for unsteady flow in porous media. Discrete and Continuous Dynamical Systems - B, 2015, 20 (7) : 2171-2185. doi: 10.3934/dcdsb.2015.20.2171
[16]

T. L. van Noorden, I. S. Pop, M. Röger. Crystal dissolution and precipitation in porous media: L$^1$-contraction and uniqueness. Conference Publications, 2007, 2007 (Special) : 1013-1020. doi: 10.3934/proc.2007.2007.1013
[17]

D. G. Aronson. Self-similar focusing in porous media: An explicit calculation. Discrete and Continuous Dynamical Systems - B, 2012, 17 (6) : 1685-1691. doi: 10.3934/dcdsb.2012.17.1685
[18]

Maurizio Verri, Giovanna Guidoboni, Lorena Bociu, Riccardo Sacco. The role of structural viscoelasticity in deformable porous media with incompressible constituents: Applications in biomechanics. Mathematical Biosciences & Engineering, 2018, 15 (4) : 933-959. doi: 10.3934/mbe.2018042
[19]

Olivier Pironneau, Alexei Lozinski, Alain Perronnet, Frédéric Hecht. Numerical zoom for multiscale problems with an application to flows through porous media. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 265-280. doi: 10.3934/dcds.2009.23.265
[20]

Alexei Heintz, Andrey Piatnitski. Osmosis for non-electrolyte solvents in permeable periodic porous media. Networks and Heterogeneous Media, 2016, 11 (3) : 471-499. doi: 10.3934/nhm.2016005

 Impact Factor: 

Tools

Metrics

  • PDF downloads (30)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy