Numerical Solution of Nonlinear Reaction–Advection–Diffusion Equation
作者： Anup Singh , S. Das , S. H. Ong , H. Jafari
DOI: 10.1115/1.4042687
关键词:
摘要: In the present article, the advection–diffusion equation (ADE) having a nonlinear type source/sink term with initial and boundary conditions is solved using finite difference method (FDM). The solution of solute concentration is calculated numerically and also presented graphically for conservative and nonconservative cases. The emphasis is given for the stability analysis, which is an important aspect of the proposed mathematical model. The accuracy and efficiency of the proposed method are validated by comparing the results obtained with existing analytical solutions for a conservative system. The novelty of the article is to show the damping nature of the solution profile due to the presence of the nonlinear reaction term for different particular cases in less computational time by using the reliable and efficient finite difference method.
asme.org
sci-hub.se 参考文章(18)
M. Thangarajan, Groundwater Models and Their Role in Assessment and Management of Groundwater Resources and Pollution Springer, Dordrecht. pp. 189- 236 ,(2007) , 10.1007/978-1-4020-5729-8_8
M. Th. van Genuchten, W. J. Alves, Analytical solutions of the one-dimensional convective-dispersive solute transport equation United States. Dept. of Agriculture. Technical bulletin (USA). ,(1982) , 10.22004/AG.ECON.157268
José Francisco Gómez-Aguilar, Margarita Miranda-Hernández, MG López-López, Victor Manuel Alvarado-Martínez, Dumitru Baleanu, None, Modeling and simulation of the fractional space-time diffusion equation Communications in Nonlinear Science and Numerical Simulation. ,vol. 30, pp. 115- 127 ,(2016) , 10.1016/J.CNSNS.2015.06.014
Eliezer J. Wexler, Analytical solutions for one-, two-, and three-dimensional solute transport in ground-water systems with uniform flow Techniques of water-resources investigations. ,(1989) , 10.3133/OFR8956
Jacob Bear, Arnold Verruijt, Modeling groundwater flow and pollution ,(1987)
F. De Smedt, Analytical solutions of the one-dimensional convective-dispersive solute transport equation: M.Th. van Genuchten and W.J. Alves. Technical bulletin no. 1661, U.S. Department of Agriculture, Washington, DC, 1982. 151 pp Agricultural Water Management. ,vol. 9, pp. 79- 80 ,(1984) , 10.1016/0378-3774(84)90020-9
Francisco de la Hoz, Fernando Vadillo, The solution of two-dimensional advection–diffusion equations via operational matrices Applied Numerical Mathematics. ,vol. 72, pp. 172- 187 ,(2013) , 10.1016/J.APNUM.2013.06.006
Alexandar Djordjevich, Svetislav Savović, Solute transport with longitudinal and transverse diffusion in temporally and spatially dependent flow from a pulse type source International Journal of Heat and Mass Transfer. ,vol. 65, pp. 321- 326 ,(2013) , 10.1016/J.IJHEATMASSTRANSFER.2013.06.002
Shahid S. Siddiqi, Saima Arshed, Quintic B-spline for the numerical solution of the good Boussinesq equation Journal of the Egyptian Mathematical Society. ,vol. 22, pp. 209- 213 ,(2014) , 10.1016/J.JOEMS.2013.06.015
Mehdi Dehghan, Numerical solution of the three-dimensional advection-diffusion equation Applied Mathematics and Computation. ,vol. 150, pp. 5- 19 ,(2004) , 10.1016/S0096-3003(03)00193-0