A Novel Method for Solving Time-Dependent 2D Advection-Diffusion-Reaction Equations to Model Transfer in Nonlinear Anisotrophic Media
Document Type
Article
Publication Date
7-1-2019
Department
Mathematics
School
Mathematics and Natural Sciences
Abstract
This paper presents a new numerical technique for solving initial and boundary value problems with unsteady strongly nonlinear advection diffusion reaction (ADR) equations. The method is based on the use of the radial basis functions (RBF) for the approximation space of the solution. The Crank-Nicolson scheme is used for approximation in time. This results in a sequence of stationary nonlinear ADR equations. The equations are solved sequentially at each time step using the proposed semi-analytical technique based on the RBFs. The approximate solution is sought in the form of the analytical expansion over basis functions and contains free parameters. The basis functions are constructed in such a way that the expansion satisfies the boundary conditions of the problem for any choice of the free parameters. The free parameters are determined by substitution of the expansion in the equation and collocation in the solution domain. In the case of a nonlinear equation, we use the well-known procedure of quasilinearization. This transforms the original equation into a sequence of the linear ones on each time layer. The numerical examples confirm the high accuracy and robustness of the proposed numerical scheme.
Publication Title
Communications In Computational Physics
Volume
26
Issue
1
First Page
233
Last Page
264
Recommended Citation
Lin, J.,
Reutskiy, S.,
Chen, C.,
Lu, J.
(2019). A Novel Method for Solving Time-Dependent 2D Advection-Diffusion-Reaction Equations to Model Transfer in Nonlinear Anisotrophic Media. Communications In Computational Physics, 26(1), 233-264.
Available at: https://aquila.usm.edu/fac_pubs/16977