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

Acta Geophysica

Volumn 55, Issue 1, 2007, Pages 104-118

  Kalinowska, Monika B ^a   Rowiński, Paweł M ^a  

^a INSTITUTE OF GEOPHYSICS   (Poland)

Author keywords

Advection diffusion equation; Modified Equation approach; Numerical diffusion; Numerical dispersion; Truncation error

Indexed keywords

APPROXIMATION THEORY; DIFFUSION IN LIQUIDS; DISPERSIONS; FINITE DIFFERENCE METHOD; PARTIAL DIFFERENTIAL EQUATIONS;

ADVECTION-DIFFUSION EQUATION; MODIFIED EQUATION APPROACH; NUMERICAL DIFFUSION; NUMERICAL DISPERSION; TRUNCATION ERROR;

OPEN CHANNEL FLOW;

ADVECTION-DIFFUSION EQUATION; DIFFUSION; DISPERSION; FINITE DIFFERENCE METHOD; OPEN CHANNEL FLOW; TWO-DIMENSIONAL MODELING;

EID: 33845912176     PISSN: 18956572     EISSN: 18957455     Source Type: Journal    
DOI: 10.2478/s11600-006-0046-3     Document Type: Article

References (12)

1. Ataie-Ashtiani, B., and S.A. Hosseini, 2005, Error analysis of finite difference methods for two-dimensional advection-dispersion-reaction equation, Advances in Water Resources 28, 793-806.
2. 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.
3. Fletcher, C.A.J., 1991, Computational Techniques for Fluid Dynamics, Springer-Verlag, Berlin.
4. Grima, R., and T.J. Newman, 2004, Accurate discretization of advection-diffusion equations, Physical Review E 70, 036703.
5. 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.
6. Kalinowska, M.B., and P.M. Rowiński, 2004, Comparison of numerical schemes for two-dimensional mixing models for rivers, XXIV International School of Hydraulics, Hydraulic Problems in Environmental Engineering, Gdańsk, 97-104.
7. MacKenzie, T., and A.J. Roberts, 2003, Holistic discretization of shear dispersion in a two-dimensional channel, Journal of the Australian Mathematical Society 44, E, C512-C530.
8. 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.
9. Szymkiewicz, R., 2000, Mathematical Modeling of the Flow in Rivers and Channels (in Polish), PWN, Warszawa.
10. Szymkiewicz, R., 2006, Method of Investigation of Numerical Diffusion and Dispersion in Solutions of Hydrodynamic Equations (in Polish), Wydawnictwo Politechniki Gdańskiej, Gdańsk.
11. Thomas, J.W., 1995, Numerical Partial Differential Equations, Finite Difference Methods, Springer, New York.
12. 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.