Controlling numerical diffusion in solving advection-dominated transport problems

Nicolae Suciu; Imre Boros

doi:10.33993/jnaat531-1438

Authors

Nicolae Suciu Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania https://orcid.org/0000-0001-7436-8463
Imre Boros Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania https://orcid.org/0000-0003-2568-4640

DOI:

https://doi.org/10.33993/jnaat531-1438

Keywords:

Advection-dominated transport, Numerical diffusion, Finite differences, Method of lines, Global random walk

Abstract views: 146

Abstract

Numerical schemes for advection-dominated transport problems are are evaluated in a comparative study. Explicit and implicit finite difference methods are analyzed together with a global random walk algorithm in the frame of a splitting procedure. The efficiency of the methods with respect to the control of the numerical diffusion is investigated numerically on one-dimensional problems with constant coefficients and two-dimensional problems with variable coefficients consisting of realizations of space-random functions.

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References

D.L. Book, C. Li, G. Patnaik and F.F. Grinstein, Quantifying residual numerical diffusion in flux-corrected transport algorithms, J. Sci. Comp. 6(3) (1991), 323–243. https://dx.doi.org/10.1007/BF01062816 DOI: https://doi.org/10.1007/BF01062816

F. Brunner, F.A. Radu, M. Bause and P. Knabner, Optimal order convergence of a modified BDM1 mixed finite element scheme for reactive transport in porous media, Adv. Water Resour. 35 (2012), 163–171. https://dx.doi.org/10.1016/j.advwatres.2011.10.001 DOI: https://doi.org/10.1016/j.advwatres.2011.10.001

C.J.M. Hewett, Consistency and numerical diffusion (2021). https://www.youtube.com/watch?v=Cjb4YtgeIn0&t=263s

P. Knabner and L. Angermann, Numerical methods for elliptic and parabolic partial differential equations, Springer, New York, 2003. https://doi.org/10.1007/b97419 DOI: https://doi.org/10.1007/b97419

D. Kuzmin, Explicit and implicit FEM-FCT algorithms with flux linearization, J. Comput. Phys. 228(7) (2009), 2517–2534. https://dx.doi.org/10.1016/j.jcp.2008.12.011 DOI: https://doi.org/10.1016/j.jcp.2008.12.011

D. Kuzmin, A. Hannukainen and S. Korotov, A new a posteriori error estimate for convection-reaction-diffusion problems, J. Comput. Appl. Math. 218(1) (2008), 70–78. https://dx.doi.org/10.1016/j.cam.2007.04.033 DOI: https://doi.org/10.1016/j.cam.2007.04.033

M. Ohlberger and C. Rohde, Adaptive finite volume approximations of weakly coupled convection dominated parabolic systems, IMA J. Numer. Anal. 22(2) (2002), 253–280. https://dx.doi.org/10.1093/imanum/22.2.253 DOI: https://doi.org/10.1093/imanum/22.2.253

F.A. Radu, N. Suciu, J. Hoffmann, A. Vogel, O. Kolditz, C-H. Park and S. Attinger, Accuracy of numerical simulations of contaminant transport in heterogeneous aquifers: a comparative study, Adv. Water Resour. 34 (2011), 47–61. https://dx.doi.org/10.1016/j.advwatres.2010.09.012 DOI: https://doi.org/10.1016/j.advwatres.2010.09.012

W.E. Schiesser and G.W. Griffiths, A compendium of partial differential equation models: method of lines analysis with Matlab, Cambridge University Press, 2009. https://doi.org/10.1017/CBO9780511576270 DOI: https://doi.org/10.1017/CBO9780511576270

J.C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, SIAM, 2004. https://doi.org/10.1137/1.9780898717938 DOI: https://doi.org/10.1137/1.9780898717938

N. Suciu, Diffusion in random velocity fields with applications to contaminant transport in groundwater, Adv. Water Resour. 69 (2014), 114–133. http://dx.doi.org/10.1016/j.advwatres.2014.04.002 DOI: https://doi.org/10.1016/j.advwatres.2014.04.002

N. Suciu, Diffusion in Random Fields. Applications to Transport in Groundwater, Birkhäuser, Cham, 2019. https://doi.org/10.1007/978-3-030-15081-5 DOI: https://doi.org/10.1007/978-3-030-15081-5

N. Suciu, L. Schüler, S. Attinger and P. Knabner, Towards a filtered density function approach for reactive transport in groundwater, Adv. Water Resour. 90 (2016), 83–98. https://dx.doi.org/10.1016/j.advwatres.2016.02.016 DOI: https://doi.org/10.1016/j.advwatres.2016.02.016

C. Vamoș, N. Suciu and H. Vereecken, Generalized random walk algorithm for the numerical modeling of complex diffusion processes, J. Comput. Phys. 186 (2003), 527–544. https://doi.org/10.1016/S0021-9991(03)00073-1 DOI: https://doi.org/10.1016/S0021-9991(03)00073-1