Simulation of linear and nonlinear advection-diffusion problems by the direct radial basis function collocation method

被引：10
|
作者：
Zhang, Juan [1 ,2 ]
Wang, Fuzhang [3 ]
Nadeem, Sohail [4 ]
Sun, Mei [5 ]
机构：
[1] China Univ Min & Technol, Sch Informat & Control Engn, Xuzhou 221116, Jiangsu, Peoples R China
[2] Guangdong ATV Vocat Coll Performing Arts, Dongguan 523710, Peoples R China
[3] Nanchang Inst Technol, Nanchang 330044, Jiangxi, Peoples R China
[4] Quaid I Azam Univ, Dept Math, Islamabad 44000, Pakistan
[5] Huaibei Normal Univ, Coll Comp Sci & Technol, Huaibei 235000, Peoples R China
来源：
INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER | 2022年 / 130卷
关键词：
Advection-diffusion equation; Multiquadric; Collocation method; Meshless; Nonlinear problems; KANSA RBF METHOD;
D O I：
10.1016/j.icheatmasstransfer.2021.105775
中图分类号：
O414.1 [热力学];
学科分类号：
摘要：
A simple direct radial basis function collocation method is proposed for the advection-diffusion equations. First, a new scheme of multiquadric radial basis function (RBF) is proposed. Then, the newly-proposed radial basis function can be directly used to deal with the time variable as well as space variables encountered in the advection-diffusion equations. This is realized by considering conventional time steps as collocation points. Numerical results for several advection-diffusion equations with different values of Pe ' clet numbers show that the direct radial basis function collocation method performs well for both linear and nonlinear cases.
引用
收藏
页数：6
相关论文
共 50 条
  • [1] Space-time radial basis function collocation method for one-dimensional advection-diffusion problem
    Khaksarfard, Marzieh
    Ordokhani, Yadollah
    Hashemi, Mir Sajjad
    Karimi, Kobra
    COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, 2018, 6 (04): : 426 - 437
  • [2] A nonlinear subgrid method for advection-diffusion problems
    Santos, Isaac P.
    Almeida, Regina C.
    COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2007, 196 (45-48) : 4771 - 4778
  • [3] Solution of the linear and nonlinear advection-diffusion problems on a sphere
    Skiba, Yuri N.
    Cruz-Rodriguez, Roberto C.
    Filatov, Denis M.
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2020, 36 (06) : 1922 - 1937
  • [4] A hybrid radial basis functions collocation technique to numerically solve fractional advection-diffusion models
    Hussain, Manzoor
    Haq, Sirajul
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2020, 36 (06) : 1254 - 1279
  • [5] Meshfree explicit local radial basis function collocation method for diffusion problems
    Sarler, B.
    Vertnik, R.
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2006, 51 (08) : 1269 - 1282
  • [6] Meshless simulation of stochastic advection-diffusion equations based on radial basis functions
    Dehghan, Mehdi
    Shirzadi, Mohammad
    ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2015, 53 : 18 - 26
  • [7] A Meshless Method for Advection-Diffusion Problems
    Xue, Dangqin
    Zhao, Huanping
    Zhang, Jiaxi
    Hou, Shulin
    ENERGY DEVELOPMENT, PTS 1-4, 2014, 860-863 : 1594 - +
  • [8] Localized radial basis function collocation method for long-time simulation of nonlinear transient heat conduction problems
    Wang, Yikun
    Jing, Xiaohan
    Qiu, Lin
    APPLIED MATHEMATICS LETTERS, 2025, 165
  • [9] Towards stable radial basis function methods for linear advection problems
    Glaubitz, Jan
    Le Meledo, Elise
    Oeffner, Philipp
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2021, 85 : 84 - 97
  • [10] The decomposition method for Cauchy advection-diffusion problems
    Lesnic, D
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2005, 49 (04) : 525 - 537
12345