Space–Time Radial Basis Function–Based Meshless Approach for Solving Convection–Diffusion Equations

Cheng-Yu Ku, Jing-En Xiao and Chih-Yu Liu
Additional contact information
Cheng-Yu Ku: Department of Harbor and River Engineering, School of Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan
Jing-En Xiao: Center of Excellence for Ocean Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan
Chih-Yu Liu: Department of Harbor and River Engineering, School of Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan

Mathematics, 2020, vol. 8, issue 10, 1-23

Abstract: This article proposes a space–time meshless approach based on the transient radial polynomial series function (TRPSF) for solving convection–diffusion equations. We adopted the TRPSF as the basis function for the spatial and temporal discretization of the convection–diffusion equation. The TRPSF is constructed in the space–time domain, which is a combination of n –dimensional Euclidean space and time into an n + 1–dimensional manifold. Because the initial and boundary conditions were applied on the space–time domain boundaries, we converted the transient problem into an inverse boundary value problem. Additionally, all partial derivatives of the proposed TRPSF are a series of continuous functions, which are nonsingular and smooth. Solutions were approximated by solving the system of simultaneous equations formulated from the boundary, source, and internal collocation points. Numerical examples including stationary and nonstationary convection–diffusion problems were employed. The numerical solutions revealed that the proposed space–time meshless approach may achieve more accurate numerical solutions than those obtained by using the conventional radial basis function (RBF) with the time-marching scheme. Furthermore, the numerical examples indicated that the TRPSF is more stable and accurate than other RBFs for solving the convection–diffusion equation.

Keywords: space–time; transient radial basis function; convection–diffusion equation; meshless; radial polynomials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/10/1735/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/10/1735/ (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:8:y:2020:i:10:p:1735-:d:425795

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 ().