A Hybrid Interpolating Meshless Method for 3D Advection–Diffusion Problems

Zhijuan Meng, Xiaofei Chi and Lidong Ma
Additional contact information
Zhijuan Meng: School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China
Xiaofei Chi: School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China
Lidong Ma: School of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, China

Mathematics, 2022, vol. 10, issue 13, 1-21

Abstract: A hybrid interpolating meshless (HIM) method is established for dealing with three-dimensional (3D) advection–diffusion equations. To improve computational efficiency, a 3D equation is changed into correlative two-dimensional (2D) equations. The improved interpolating moving least-squares (IIMLS) method is applied in 2D subdomains to obtain the required approximation function with interpolation property. The finite difference method (FDM) is utilized in time domain and the splitting direction. Setting diagonal elements to one in the coefficient matrix is chosen to directly impose Dirichlet boundary conditions. Using the HIM method, difficulties created by the singularity of the weight functions, such as truncation error and calculation inconvenience, are overcome. To prove the advantages of the new method, some advection–diffusion equations are selected and solved by HIM, dimension splitting element-free Galerkin (DSEFG), and improved element-free Galerkin (IEFG) methods. Comparing and analyzing the calculation results of the three methods, it can be shown that the HIM method effectively improves computation speed and precision. In addition, the effectiveness of the HIM method in the nonlinear problem is verified by solving a 3D Richards’ equation.

Keywords: hybrid interpolating meshless method; nonsingular weight function; advection–diffusion equation; finite difference method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/13/2244/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/13/2244/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:13:p:2244-:d:848848

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().