Solution of the advection-diffusion equation using the Differential Quadrature Method

KSCE Journal of Civil Engineering

Volumn 14, Issue 1, 2010, Pages 69-75

  Kaya, Birol ^a  

^a DOKUZ EYLUL UNIVERSITY   (Turkey)

Author keywords

Advection diffusion equation; Differential quadrature method; Explicit; Finite differences method; Implicit; Numerical solution

Indexed keywords

DIFFERENTIATION (CALCULUS); DIFFUSION; FINITE DIFFERENCE METHOD; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS;

ADVECTION-DIFFUSION EQUATION; DIFFERENTIAL QUADRATURE METHODS; EXPLICIT; FINITE DIFFERENCES METHODS; IMPLICIT; NUMERICAL SOLUTION;

ADVECTION;

EID: 70350227155     PISSN: 12267988     EISSN: 19763808     Source Type: Journal    
DOI: 10.1007/s12205-010-0069-9     Document Type: Article

References (27)

1. Al-Saif, A. S. J. and Zheng-You, Z. (2003). Application of mixed differential quadrature method for solving the coupled two-dimensional incompressible Navier-stokes equation and heat equation. Journal of Shanghai University (English Edition), Vol. 7, No. 4, pp. 343-351.
2. Baeumer, B., Benson, D. A., Meerschaert, M. M., and Wheatcraft, S. W. (2001). Subordinated advection-dispersion equation for contaminant transport. Water Resources Research, Vol. 37, No. 6, pp. 1543-1550.
3. Bajracharya, K. and Barry, D. A. (1997). Accuracy criteria for linearized diffusion wave flood routing. Journal of Hydrology, Vol. 195, pp. 200-217.
4. Bellman, R. and Casti, J. (1971). Differential quadrature and long-term integration. Journal of Mathematical Analysis and Applications. Vol. 34,Issue 2, pp. 235-238.
5. Bert, C. W. and Malik, M. (1996). Differential quadrature method in computational mechanics: A review. Applied Mechanics Review, Vol. 49, No. 1, pp. 1-28.
6. Civalek, Ö. (2003). Linear and non-linear dynamic analysis of multi-degree-of-freedom systems by harmonic differential quadrature method (in Turkish), PhD Thesis, Izmir, Dokuz Eylul University, Graduate School of Natural and Applied Sciences.
7. Civalek, Ö. (2004). Application of Dierential Quadrature (DQ) and Harmonic Dierential Quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns. Engineering Structures, Elsevier, Vol. 26,Issue 2, pp. 171-186.
8. Dehghan, M. (2004). Weighted nite difference techniques for the one-dimensional advection-diffusion equation. Applied Mathematics and Computation, Vol. 147,Issue 2, pp. 307-319.
9. Enrique, P., Emilio, D., Rosell'o, M. D., and Romero, J. V. (2008). A stable numerical method for solving variable coefficient advection-diffusion models. Computers and Mathematics with Applications, Vol. 56,Issue 3, pp. 754-768.
10. Gane, C. R. and Stephenson, P. L. (1979). An explicit numerical method for solving transient combined heat conduction and convection problems. Int. J. Numer. Meth. Eng., Vol. 14, No. 8, pp. 1141-1163.
11. Geiser, J. (2007). Analytical solutions for convection-diffusion-dispersion-reaction-equations with different retardation-factors and applications in 2d and 3d. Hikari Ltd., International Mathematical Forum, Vol. 2, No. 44, pp. 2179-2205.
12. Hongxing, R. (2008). A conservative characteristic finite volume element method for solution of the advection-diffusion equation. Comput. Methods Appl. Mech. Engrg., Vol. 197, pp. 3862-3869.
13. Park, Y. S. and Baik, J. J. (2008). Analytical solution of the advection-diffusion equation for a ground-level finite area source. Atmospheric Environment, doi: 10.1016/j.atmosenv.2008.09.019.
14. Revelli, R. and Ridolfi, L. (2008). Generalized collocation method for two-dimensional reaction-diffusion problems with homogeneous Neumann boundary conditions. Computers and Mathematics with Applications, Elsevier, Vol. 56,Issue 9, pp. 2360-2370.
15. Roop, J. P. (2008). Numerical approximation of a one-dimensional space fractional advection-dispersion equation with boundary layer. Computers and Mathematics with Applications, Vol. 56,Issue 7, pp. 1808-1819.
16. Schlegel, M., Knotha, O., Arnoldb, M., and Wolke, R. (2008). Multirate Runge-Kutta schemes for advection equations. Journal of Computational and Applied Mathematics, doi:10.1016/j.cam. 2008.08.009.
17. Shu, C. (2000). Dierential quadrature and its application in engineering, Springer-Verlag London Limited.
18. Shu, C. and Chew, Y. T. (1997). Fourier expansion-based differential quadrature and its application to Helmholtz eigenvalue problems. Communications in Numerical Methods in Engineering, Vol. 13, pp. 643-653.
19. Shu, C. and Richards, B. E. (1992). Application of generalized differential quadrature to solve two-dimensional incompressible navierstokes equations. International Journal for Numerical Methods in Fluids, Vol. 15,Issue 7, pp. 791-798.
20. Shu, C., Wang, L., Chew, Y. T., and Zhao, N. (2004). Numerical study of eccentric Couette-Taylor flows and effect of eccentricity on flow patterns. Theoret. Comput. Fluid Dynamics, Vol. 18, No. 1, pp. 43-59.
21. Shu, C. and Xue, H. (1997). Explicit computations of weighting coefficients in the harmonic differential quadrature. Journal of Sound and Vibration, Vol. 204, No. 3, pp. 549-555.
22. Shu, C., Yao, Q., Yeo, K. S., and Zhu, Y. D. (2002). Numerical analysis of flow and thermal fields in arbitrary eccentric annulus by differential quadrature method. Heat and Mass Transfer, Springer-Verlag, Vol. 38,No. 7-8, pp. 597-608.
23. Temsah, R. S. (2009). Numerical solutions for convection-diffusion equation using El-Gendi method. Communications in Nonlinear Science and Numerical Simulation, Vol. 14,Issue 3, pp. 760-769.
24. Tian, Z. F. and Dai, S. Q. (2007). High-order compact exponential finite difference methods for convection-diffusion type problems. Journal of Computational Physics, Vol. 220,Issue 2, pp. 952-974.
25. Yeh, H. D. and Yeh, G. T. (2007). Analysis of point-source and boundary-source solutions of one-dimensional groundwater transport equation. ASCE Journal of Environmental Engineering, ASCE, Vol. 133, No. 11, pp. 1032-1041.
26. Yen, B. C. and Tsai, C. W. (2001). On noninertia wave versus diffusion wave in flood routing. Journal of Hydrology, Vol. 244, pp. 97-104.
27. Younes, A. and Ackerer, P. (2005). Solving the advection-diusion equation with the Eulerian-Lagrangian localized adjoint method on unstructured meshes and non uniform time stepping. Journal of Computational Physics, Elsevier,Vol. 208,Issue 1, pp. 384-402.