Abstract
In this paper we discuss numerical method for a pore scale model for precipitation and dissolution in porous media.We focus here on the chemistry, which is modeled by a parabolic problem that is coupled through the boundary conditions to an ordinary differential inclusion. A semi-implicit time stepping is combined with a regularization approach to construct a stable and convergent numerical scheme. For dealing with the emerging time discrete nonlinear problems we propose here a simple fixed point iterative procedure.
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References
Devigne, V.M.: Ecoulements et Conditions aux Limites Particulières Appliqu ées en Hydrogéologie et Théorie Mathématique des Processus de Dissolution/Précipitation en Milieux Poreaux. Ph'D thesis, Université Lyon 1 (2006)
van Duijn, C.J., Pop, I.S.: Crystal dissolution and precipitation in porous media: pore scale analysis. J. Reine Angew. Math. 577, 171–211 (2004)
van Duijn, C.J., Knabner, P.: Travelling wave behaviour of crystal dissolution in porous media flow. European J. Appl. Math. 8, 49–72 (1997)
Hornung, U., Jäger, W.: A model for chemical reactions in porous media. In: Warnatz, J., Jäger, W. (eds.) Complex Chemical Reaction Systems. Mathematical Modeling and Simulation. Chemical Physics 47, Springer, Berlin, (1987)
Hornung, U., Jäger, W.: Diffusion, convection, adsorption, and reaction of chemicals in porous media. J. Differ. Equations 92, 199–225 (2001)
Hornung, U., Jäger, W., Mikelić, A: Reactive transport through an array of cells with semipermeable membranes. RAIRO Modél. Math. Anal. Numér. 28, 59–94 (1994)
Knabner, P., van Duijn, C.J., Hengst, S.: An analysis of crystal dissolution fronts in flows through porous media. Part 1: Compatible boundary conditions. Adv. Water Res. 18, 171–185 (1995)
Knobloch, P.: On the application of the pmod 1 element to incompressible flow problems. Comput. Vis. Sci. 6, 185–195 (2004)
Pop, I.S., Radu, F., Knabner, P.: Mixed finite elements for the Richards' equation: linearization procedure. J. Comput. Appl. Math. 168, 365–373 (2004)
Pop, I.S., Yong, W.A.: On the existence and uniqueness of a solution for an elliptic problem. Studia Univ. Babeş-Bolyai Math. 45, 97–107 (2000)
Russo, A.: Bubble stabilization of finite element methods for the linearized incompressible Navier-Stokes equations. Comput. Methods appl. Mech. Engrg. 132, 335–343 (1996)
Slodička, M.: A robust and effcient linearization scheme for doubly nonlinear and degenerate parabolic problems arising in flow in porous media. SIAM J. Sci. Comput. 23, 1593–1614 (2002)
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Pop, I., Devigne, V., van Duijn, C., Clopeau, T. (2006). A Numerical Scheme for the Micro Scale Dissolution and Precipitation in Porous Media. In: de Castro, A.B., Gómez, D., Quintela, P., Salgado, P. (eds) Numerical Mathematics and Advanced Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34288-5_30
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DOI: https://doi.org/10.1007/978-3-540-34288-5_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34287-8
Online ISBN: 978-3-540-34288-5
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