TY - JOUR
T1 - A Novel Method for Solving Time-Dependent 2D Advection-Diffusion-Reaction Equations to Model Transfer in Nonlinear Anisotropic Media
AU - Ji Lin, Sergiy Reutskiy, C. S. Chen & Jun Lu
JO - Communications in Computational Physics
VL - 1
SP - 233
EP - 264
PY - 2019
DA - 2019/02
SN - 26
DO - http://doi.org/10.4208/cicp.OA-2018-0005
UR - https://global-sci.org/intro/article_detail/cicp/13033.html
KW - Advection diffusion reaction, time-dependent, fully nonlinear, anisotropic media,
Crank-Nicolson scheme, meshless method.
AB - <p style="text-align: justify;">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.</p>