Details
| Original language | English |
|---|---|
| Article number | 109875 |
| Journal | Journal of computational physics |
| Volume | 426 |
| Early online date | 12 Oct 2020 |
| Publication status | Published - 1 Feb 2021 |
Abstract
In the recent decade, meshless methods have been handled for solving some PDEs due to their easiness. One of the most efficient meshless methods is the element free Galerkin (EFG) method. The test and trial functions of the EFG are based upon the special basis. Recently, some modifications have been developed to improve the EFG method. One of these improvements is the variational multiscale EFG (VMEFG) procedure. In the current article, the shape functions of interpolating moving least squares (IMLS) approximation are applied to the variational multiscale EFG technique to numerical study the Navier–Stokes equations coupled with a heat transfer equation such that this model is well-known as two-dimensional nonstationary Boussinesq equations. In order to reduce the computational time of simulation, we employ a reduced order model (ROM) based on the proper orthogonal decomposition (POD) technique. In the current paper, we developed a new reduced order model based on the meshless numerical procedure for solving an important model in fluid mechanics. To illustrate the reduction in CPU time as well as the efficiency of the proposed method, we investigate two-dimensional cases.
Keywords
- Element free Galerkin and proper orthogonal decomposition methods, Incompressible Navier–Stokes and nonstationary incompressible Boussinesq equations, Interpolating moving least squares approximation and Meshless methods, Large scale atmospheric and oceanic flows, Rayleigh-Benard convection problem, Variational multiscale approach
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Modelling and Simulation
- Physics and Astronomy(all)
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- General Physics and Astronomy
- Computer Science(all)
- Computer Science Applications
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Journal of computational physics, Vol. 426, 109875, 01.02.2021.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A reduced-order variational multiscale interpolating element free Galerkin technique based on proper orthogonal decomposition for solving Navier–Stokes equations coupled with a heat transfer equation
T2 - Nonstationary incompressible Boussinesq equations
AU - Abbaszadeh, Mostafa
AU - Dehghan, Mehdi
AU - Khodadadian, Amirreza
AU - Noii, Nima
AU - Heitzinger, Clemens
AU - Wick, Thomas
N1 - Funding Information: The authors are very grateful to the reviewers for carefully reading this paper and for their comments and suggestions which have improved the paper. A. Khodadadian and C. Heitzinger acknowledge financial support by FWF Austrian Science Fund START Project no. Y660 PDE Models for Nanotechnology.
PY - 2021/2/1
Y1 - 2021/2/1
N2 - In the recent decade, meshless methods have been handled for solving some PDEs due to their easiness. One of the most efficient meshless methods is the element free Galerkin (EFG) method. The test and trial functions of the EFG are based upon the special basis. Recently, some modifications have been developed to improve the EFG method. One of these improvements is the variational multiscale EFG (VMEFG) procedure. In the current article, the shape functions of interpolating moving least squares (IMLS) approximation are applied to the variational multiscale EFG technique to numerical study the Navier–Stokes equations coupled with a heat transfer equation such that this model is well-known as two-dimensional nonstationary Boussinesq equations. In order to reduce the computational time of simulation, we employ a reduced order model (ROM) based on the proper orthogonal decomposition (POD) technique. In the current paper, we developed a new reduced order model based on the meshless numerical procedure for solving an important model in fluid mechanics. To illustrate the reduction in CPU time as well as the efficiency of the proposed method, we investigate two-dimensional cases.
AB - In the recent decade, meshless methods have been handled for solving some PDEs due to their easiness. One of the most efficient meshless methods is the element free Galerkin (EFG) method. The test and trial functions of the EFG are based upon the special basis. Recently, some modifications have been developed to improve the EFG method. One of these improvements is the variational multiscale EFG (VMEFG) procedure. In the current article, the shape functions of interpolating moving least squares (IMLS) approximation are applied to the variational multiscale EFG technique to numerical study the Navier–Stokes equations coupled with a heat transfer equation such that this model is well-known as two-dimensional nonstationary Boussinesq equations. In order to reduce the computational time of simulation, we employ a reduced order model (ROM) based on the proper orthogonal decomposition (POD) technique. In the current paper, we developed a new reduced order model based on the meshless numerical procedure for solving an important model in fluid mechanics. To illustrate the reduction in CPU time as well as the efficiency of the proposed method, we investigate two-dimensional cases.
KW - Element free Galerkin and proper orthogonal decomposition methods
KW - Incompressible Navier–Stokes and nonstationary incompressible Boussinesq equations
KW - Interpolating moving least squares approximation and Meshless methods
KW - Large scale atmospheric and oceanic flows
KW - Rayleigh-Benard convection problem
KW - Variational multiscale approach
UR - http://www.scopus.com/inward/record.url?scp=85095740607&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2020.109875
DO - 10.1016/j.jcp.2020.109875
M3 - Article
AN - SCOPUS:85095740607
VL - 426
JO - Journal of computational physics
JF - Journal of computational physics
SN - 0021-9991
M1 - 109875
ER -