A Finite Volume-Complete Flux Scheme for a Polluted Groundwater Site

We present a model of a polluted groundwater site. The model consists of a coupled system of advection-diffusion-reaction equations for the groundwater level and the concentration of the pollutant. We use the complete flux scheme for the space discretization in combination with the -method for time integration and we prove a new stability result for the scheme. Numerical results are computed for the Guarani Aquifer in South America and they show good agreement with results in literature.

[1]  ten Jhm Jan Thije Boonkkamp,et al.  Extension of the complete flux scheme to time-dependent conservation laws , 2010 .

[2]  P. Domenico,et al.  Physical and chemical hydrogeology , 1990 .

[3]  Lei Liu,et al.  The Complete Flux Scheme : error analysis and application to plasma simulation , 2011 .

[4]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[5]  E. Stitt Water Follies: Groundwater Pumping and the Fate of America's Fresh Waters , 2006 .

[6]  高等学校計算数学学報編輯委員会編 高等学校計算数学学報 = Numerical mathematics , 1979 .

[7]  Jackson Roehrig,et al.  Guarani Aquifer System – The Strategical Water Source In South America , 2006 .

[8]  Lei Liu,et al.  Mass conservative finite volume discretization of the continuity equations in multi-component mixtures , 2011, J. Comput. Phys..

[9]  P. Wesseling Principles of Computational Fluid Dynamics , 2000 .

[10]  J. H. M. ten Thije Boonkkamp,et al.  The Finite Volume-Complete Flux Scheme for Advection-Diffusion-Reaction Equations , 2011, J. Sci. Comput..

[11]  Alfio Quarteroni,et al.  Numerical Mathematics (Texts in Applied Mathematics) , 2006 .

[12]  J. Bear,et al.  Modeling groundwater flow and pollution , 1987 .

[13]  van J Jan Dijk,et al.  Efficient simulation of drift–diffusive discharges: application of the ‘complete flux scheme’ , 2014 .

[14]  Barry Koren,et al.  Flux Approximation Scheme for the Incompressible Navier-Stokes Equations Using Local Boundary Value Problems , 2015, ENUMATH.

[15]  S. A. Goorden,et al.  NPZ-model with seasonal variability of plankton population dynamics , 2011 .

[16]  P. A. Domenico,et al.  Water from low‐permeability sediments and land subsidence , 1965 .

[17]  A Zaporozec,et al.  Ground-Water pollution and its sources , 1981 .