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Truncation errors of selected finite-difference methods for two-dimensional advection-diffusion equation with mixed derivatives

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EN
Abstrakty
EN
The spread of a passive contaminant in an open-channel reach is considered with use of a two-dimensional advection-diffusion equation with the included offdiagonal dispersion coefficients. This paper presents the calculation of truncation errors, namely numerical diffusion and numerical dispersion for various finite difference schemes. The accuracy of the considered finite-difference approximations is analysed by deriving and studying the relevant modified partial differential equation.
Czasopismo
Rocznik
Strony
107--118
Opis fizyczny
Twórcy
Bibliografia
  • Ataie-Ashtiani, B., and S.A. Hosseini, 2005, Error analysis of finite difference methods for twodimensional advection-dispersion-reaction equation, Advances in Water Resources 28, 793-806.
  • Bielecka-Kieloch, M., 1998, Numerical diffusion and dispersion tensor for 2-D linear advection equation, Archives of Hydro-Engineering and Environmental Mechanics 45, 1-4, 29-43.
  • Fletcher, C.A.J., 1991, Computational Techniques for Fluid Dynamics, Springer-Verlag, Berlin.
  • Grima, R., and T.J. Newman, 2004, Accurate discretization of advection-diffusion equations, Physical Review E 70, 036703.
  • Juntunen, J.S., and T.D. Tsiboukis, 2000, Reduction of numerical dispersion in FDTD method through artificial anisotropy, IEEE Trans. Microwave Theory and Technique 40, 4, 582-588.
  • Kalinowska, M.B., and P.M. Rowiński, 2004, Comparison of numerical schemes for twodimensional mixing models for rivers, XXIV International School of Hydraulics, Hydraulic Problems in Environmental Engineering, Gda´nsk, 97-104.
  • MacKenzie, T., and A.J. Roberts, 2003, Holistic discretization of shear dispersion in a twodimensional channel, Journal of the Australian Mathematical Society 44, E, C512-C530.
  • Rowiński, P.M., and M.B. Kalinowska, 2006, Admissible and inadmissible simplifications of pollution transport equations, River Flow 2006, Proceedings of the International Conference on Fluvial Hydraulics, 6-8 Sept 2006, Lisbon, 199-208.
  • Szymkiewicz, R., 2000, Mathematical Modeling of the Flow in Rivers and Channels (in Polish), PWN, Warszawa.
  • Szymkiewicz, R., 2006, Method of Investigation of Numerical Diffusion and Dispersion in Solutions of Hydrodynamic Equations (in Polish), Wydawnictwo Politechniki Gdańskiej, Gdańsk.
  • Thomas, J.W., 1995, Numerical Partial Differential Equations, Finite Difference Methods, Springer, New York.
  • Warming R.F., and B.J. Hyett 1974, The modified equation approach to the stability and accuracy analysis of finite-difference methods, J. Computational Phys. 14, 159-179.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BSL7-0021-0012
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