Abstract
In this paper, we propose an operator splitting method for convection-dominated transport equations with nonlinear reactions, which model groundwater contaminant biodegradation and many other interesting applications. The proposed method can be efficiently implemented by applying software integration techniques such as dynamical link library (DLL) or component object model (COM). Numerical results are also included to demonstrate the performance of the method.
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References
Bertolazzi, E., Manzini, G.: P2MESH: Generic objected-oriented interface between 2-d unstructured meshes and FEM/FVM-based PDE solvers. ACM Transactions on Mathematical Softwares, 28, 101–131 (2002)
Celia, M.A., Kindred, J.S., Herrera, I.: Contaminant transport and biodegradation 1. a numerical model for reactive transport in porous media. Water Resources Research, 25, 1141–1148 (1989)
Dahle, H.K., Ewing, R.E., Russell, T.F.: Eulerian-Lagrangian localized adjoint methods for a nonlinear advection-diffusion equation. Comput. Meth. Appl. Mech. Eng., 122, 223–250 (1995)
Ewing, R.E.: Upscaling of biological processes and multiphase flow in porous media. In: Fluid Flow and Transport in Porous Media: Mathematical and Numerical Treatment, Contemp. Math. 295, 195–215 (2002)
Ewing, R.E.: Operator splitting and Eulerian-Lagrangian localized adjoint methods for multiphase flow. In: The mathematics of Finite Elements and Applications, VII (Uxbridge). Academic Press, London (1991)
Karlsen, K.H., Risebro, N.H.: Corrected operator splitting for nonlinear parabolic equations. SIAM J. Numer. Anal., 37, 980–1003 (2000)
Karlsen, K.H., Risebro, N.H.: An operator splitting method for nonlinear convection-diffusion equations. Numer. Math., 77, 365–382 (1997)
Langtangen, H.P., Munthe, O.: Solving systems of partial differential equations using object-oriented programming techniques with coupled heat and fluid flow as example. ACM Transactions on Mathematical Softwares, 27, 1–26 (2001)
Lanser, D., Verwer, J.G.: Analysis of operator splitting for advection-diffusion-reaction problems from air pollution modelling. J. Comput. Appl. Math., 111, 201–216 (1999)
Wang, H., Ewing, R.E., Celia, M.A.: Eulerian-Lagrangian localized adjoint methods for reactive transport with biodegradation. Numer. Meth. Partial Diff. Eqn., 11, 229–254 (1995)
Website: Component Object Model: http://www.microsoft.com/com/
Website: libMesh: http://libmesh.sourceforge.net/
Website: OFELI: http://ofeli.sourceforge.net/
Website: VTK: http://www.vtk.org/
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Liu, J., Ewing, R.E. (2005). An Operator Splitting Method for Nonlinear Reactive Transport Equations and Its Implementation Based on DLL and COM. In: Zhang, W., Tong, W., Chen, Z., Glowinski, R. (eds) Current Trends in High Performance Computing and Its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27912-1_9
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DOI: https://doi.org/10.1007/3-540-27912-1_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25785-1
Online ISBN: 978-3-540-27912-9
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