A Novel Method for Solving Time-Dependent 2D Advection-Diffusion-Reaction Equations to Model Transfer in Nonlinear Anisotropic Media  

作　　者：Ji Lin Sergiy Reutskiy C.S.Chen Jun Lu 

机构地区：[1]State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering,International Center for Simulation Software in Engineering and Sciences,College of Mechanics and Materials,Hohai University,Nanjing 211100,China [2]State Institution"Institute of Technical Problems of Magnetism of the National Academy of Sciences of Ukraine",Industrialnaya St.,19,61106,Kharkov,Ukraine [3]Department of Mathematics,University of Southern Mississippi,Hattiesburg,MS 39406,USA [4]Nanjing Hydraulic Research Institute,Nanjing 210029,China [5]State Key Laboratory of Hydrology Water Resources and Hydraulic Engineering,Nanjing 210098,China

出　　处：《Communications in Computational Physics》2019年第6期233-264,共32页计算物理通讯（英文）

基　　金：supported by the Fundamental Research Funds for the Central Universities(No.2018B16714);the National Natural Science Foundation of China(Nos.11702083,11572111,51679150,51579153,51739008,51527811);the State Key Laboratory of Mechanics and Control of Mechanical Structures(Nanjing University of Aeronautics and Astronautics)(No.MCMS-0218G01);the China Postdoctoral Science Foundation(No.2017M611669);the China Postdoctoral Science Special Foundation(No.2018T110430);the Postdoctoral Foundation of Jiangsu Province(No.1701059C);the National Key R&D Program of China(No.2016YFC0401902);the Fund Project of NHRI(Nos.Y417002,Y417015).

摘　　要：This paper presents a new numerical technique for solving initial and bound-ary 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.

关 键 词：Advection diffusion reaction TIME-DEPENDENT fully nonlinear anisotropic media Crank-Nicolson scheme meshless method 

分 类 号：O17[理学—数学]