Asymptotic behaviour of a finite-volume scheme for the transient drift-diffusion model

2007 ◽  
Vol 27 (4) ◽  
pp. 689-716 ◽  
Author(s):  
C. Chainais-Hillairet ◽  
F. Filbet
Keyword(s):  
Asymptotic Behaviour ◽  
Diffusion Model ◽  
Finite Volume ◽  
Finite Volume Scheme ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
Volume Scheme

scholarly journals Finite-volume scheme for a degenerate cross-diffusion model motivated from ion transport

2018 ◽  
Vol 35 (2) ◽  
pp. 545-575 ◽  
Author(s):  
Clément Cancès ◽  
Claire Chainais-Hillairet ◽  
Anita Gerstenmayer ◽  
Ansgar Jüngel
Keyword(s):  
Ion Transport ◽  
Diffusion Model ◽  
Finite Volume ◽  
Finite Volume Scheme ◽  
Volume Scheme ◽  
Cross Diffusion

scholarly journals A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers

Water ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1639
Author(s):  
Abdelkrim Aharmouch ◽  
Brahim Amaziane ◽  
Mustapha El Ossmani ◽  
Khadija Talali
Keyword(s):  
Finite Volume ◽  
Coastal Aquifers ◽  
Nonlinear Partial Differential Equations ◽  
Time Integration ◽  
Mass Conservation ◽  
Coupled System ◽  
Finite Volume Scheme ◽  
Time Step ◽  
Volume Scheme ◽  
Fully Implicit

We present a numerical framework for efficiently simulating seawater flow in coastal aquifers using a finite volume method. The mathematical model consists of coupled and nonlinear partial differential equations. Difficulties arise from the nonlinear structure of the system and the complexity of natural fields, which results in complex aquifer geometries and heterogeneity in the hydraulic parameters. When numerically solving such a model, due to the mentioned feature, attempts to explicitly perform the time integration result in an excessively restricted stability condition on time step. An implicit method, which calculates the flow dynamics at each time step, is needed to overcome the stability problem of the time integration and mass conservation. A fully implicit finite volume scheme is developed to discretize the coupled system that allows the use of much longer time steps than explicit schemes. We have developed and implemented this scheme in a new module in the context of the open source platform DuMu X . The accuracy and effectiveness of this new module are demonstrated through numerical investigation for simulating the displacement of the sharp interface between saltwater and freshwater in groundwater flow. Lastly, numerical results of a realistic test case are presented to prove the efficiency and the performance of the method.

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