Finite difference approximations of multidimensional unsteady convection-diffusion-reaction equations

作者: Adem Kaya

DOI: 10.1016/J.JCP.2015.01.024

关键词:

摘要: In this paper, the numerical approximation of unsteady convection-diffusion-reaction equations with finite difference method on a special grid is studied in convection or reaction-dominated regime. We extend 19] which was designed for multidimensional steady to problems. investigate two possible different ways combining discretization time and space (where sequence discretizations interchanged). Discretization performed by using Crank-Nicolson Backward-Euler schemes, while we consider 19]. Numerical tests are presented show good performance method.

参考文章(19)
M.I. Asensio, B. Ayuso, G. Sangalli, Coupling stabilized finite element methods with finite difference time integration for advection–diffusion–reaction problems Computer Methods in Applied Mechanics and Engineering. ,vol. 196, pp. 3475- 3491 ,(2007) , 10.1016/J.CMA.2007.03.016
Javier de Frutos, Bosco García-Archilla, Volker John, Julia Novo, An adaptive SUPG method for evolutionary convection–diffusion equations Computer Methods in Applied Mechanics and Engineering. ,vol. 273, pp. 219- 237 ,(2014) , 10.1016/J.CMA.2014.01.022
Javier de Frutos, Bosco García-Archilla, Julia Novo, An adaptive finite element method for evolutionary convection dominated problems Computer Methods in Applied Mechanics and Engineering. ,vol. 200, pp. 3601- 3612 ,(2011) , 10.1016/J.CMA.2011.08.010
N. Ahmed, G. Matthies, L. Tobiska, H. Xie, Discontinuous Galerkin time stepping with local projection stabilization for transient convection–diffusion-reaction problems Computer Methods in Applied Mechanics and Engineering. ,vol. 200, pp. 1747- 1756 ,(2011) , 10.1016/J.CMA.2011.02.003
Claudio Baiocchi, Franco Brezzi, Leopoldo P. Franca, Virtual bubbles and Galerkin-least-squares type methods (Ga.L.S.) Computer Methods in Applied Mechanics and Engineering. ,vol. 105, pp. 125- 141 ,(1993) , 10.1016/0045-7825(93)90119-I
A. Kaya, A finite difference scheme for multidimensional convection-diffusion-reaction equations Computer Methods in Applied Mechanics and Engineering. ,vol. 278, pp. 347- 360 ,(2014) , 10.1016/J.CMA.2014.06.002
F. Brezzi, D. Marini, A. Russo, Applications of the pseudo residual-free bubbles to the stabilization of convection-diffusion problems Computer Methods in Applied Mechanics and Engineering. ,vol. 166, pp. 51- 63 ,(1998) , 10.1016/S0045-7825(98)00082-6
Xu-Dong Liu, Stanley Osher, Tony Chan, Weighted essentially non-oscillatory schemes Journal of Computational Physics. ,vol. 115, pp. 200- 212 ,(1994) , 10.1006/JCPH.1994.1187
L.P. Franca, A. Nesliturk, M. Stynes, On the Stability of Residual-Free Bubbles for Convection-Diffusion Problemsand their Approximation by a Two-Level Finite Element Method. Computer Methods in Applied Mechanics and Engineering. ,vol. 166, pp. 35- 49 ,(1997) , 10.1016/S0045-7825(98)00081-4