Details
| Original language | English |
|---|---|
| Pages (from-to) | 2642-2665 |
| Number of pages | 24 |
| Journal | International Journal of Numerical Methods for Heat and Fluid Flow |
| Volume | 29 |
| Issue number | 8 |
| Publication status | Published - 11 Sept 2019 |
Abstract
Purpose: The current paper aims to develop a reduced order discontinuous Galerkin method for solving the generalized Swift–Hohenberg equation with application in biological science and mechanical engineering. The generalized Swift–Hohenberg equation is a fourth-order PDE; thus, this paper uses the local discontinuous Galerkin (LDG) method for it. Design/methodology/approach: At first, the spatial direction has been discretized by the LDG technique, as this process results in a nonlinear system of equations based on the time variable. Thus, to achieve more accurate outcomes, this paper uses an exponential time differencing scheme for solving the obtained system of ordinary differential equations. Finally, to decrease the used CPU time, this study combines the proper orthogonal decomposition approach with the LDG method and obtains a reduced order LDG method. The circular and rectangular computational domains have been selected to solve the generalized Swift–Hohenberg equation. Furthermore, the energy stability for the semi-discrete LDG scheme has been discussed. Findings: The results show that the new numerical procedure has not only suitable and acceptable accuracy but also less computational cost compared to the local DG without the proper orthogonal decomposition (POD) approach. Originality/value: The local DG technique is an efficient numerical procedure for solving models in the fluid flow. The current paper combines the POD approach and the local LDG technique to solve the generalized Swift–Hohenberg equation with application in the fluid mechanics. In the new technique, the computational cost and the used CPU time of the local DG have been reduced.
Keywords
- Exponential time differencing (ETD) scheme, Local discontinuous Galerkin method, Swift–Hohenberg equation
ASJC Scopus subject areas
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computer Science Applications
- Mathematics(all)
- Applied Mathematics
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In: International Journal of Numerical Methods for Heat and Fluid Flow, Vol. 29, No. 8, 11.09.2019, p. 2642-2665.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Galerkin proper orthogonal decomposition-reduced order method (POD-ROM) for solving generalized Swift-Hohenberg equation
AU - Dehghan, Mehdi
AU - Abbaszadeh, Mostafa
AU - Khodadadian, Amirreza
AU - Heitzinger, Clemens
PY - 2019/9/11
Y1 - 2019/9/11
N2 - Purpose: The current paper aims to develop a reduced order discontinuous Galerkin method for solving the generalized Swift–Hohenberg equation with application in biological science and mechanical engineering. The generalized Swift–Hohenberg equation is a fourth-order PDE; thus, this paper uses the local discontinuous Galerkin (LDG) method for it. Design/methodology/approach: At first, the spatial direction has been discretized by the LDG technique, as this process results in a nonlinear system of equations based on the time variable. Thus, to achieve more accurate outcomes, this paper uses an exponential time differencing scheme for solving the obtained system of ordinary differential equations. Finally, to decrease the used CPU time, this study combines the proper orthogonal decomposition approach with the LDG method and obtains a reduced order LDG method. The circular and rectangular computational domains have been selected to solve the generalized Swift–Hohenberg equation. Furthermore, the energy stability for the semi-discrete LDG scheme has been discussed. Findings: The results show that the new numerical procedure has not only suitable and acceptable accuracy but also less computational cost compared to the local DG without the proper orthogonal decomposition (POD) approach. Originality/value: The local DG technique is an efficient numerical procedure for solving models in the fluid flow. The current paper combines the POD approach and the local LDG technique to solve the generalized Swift–Hohenberg equation with application in the fluid mechanics. In the new technique, the computational cost and the used CPU time of the local DG have been reduced.
AB - Purpose: The current paper aims to develop a reduced order discontinuous Galerkin method for solving the generalized Swift–Hohenberg equation with application in biological science and mechanical engineering. The generalized Swift–Hohenberg equation is a fourth-order PDE; thus, this paper uses the local discontinuous Galerkin (LDG) method for it. Design/methodology/approach: At first, the spatial direction has been discretized by the LDG technique, as this process results in a nonlinear system of equations based on the time variable. Thus, to achieve more accurate outcomes, this paper uses an exponential time differencing scheme for solving the obtained system of ordinary differential equations. Finally, to decrease the used CPU time, this study combines the proper orthogonal decomposition approach with the LDG method and obtains a reduced order LDG method. The circular and rectangular computational domains have been selected to solve the generalized Swift–Hohenberg equation. Furthermore, the energy stability for the semi-discrete LDG scheme has been discussed. Findings: The results show that the new numerical procedure has not only suitable and acceptable accuracy but also less computational cost compared to the local DG without the proper orthogonal decomposition (POD) approach. Originality/value: The local DG technique is an efficient numerical procedure for solving models in the fluid flow. The current paper combines the POD approach and the local LDG technique to solve the generalized Swift–Hohenberg equation with application in the fluid mechanics. In the new technique, the computational cost and the used CPU time of the local DG have been reduced.
KW - Exponential time differencing (ETD) scheme
KW - Local discontinuous Galerkin method
KW - Swift–Hohenberg equation
UR - http://www.scopus.com/inward/record.url?scp=85070975829&partnerID=8YFLogxK
U2 - 10.1108/HFF-11-2018-0647
DO - 10.1108/HFF-11-2018-0647
M3 - Article
AN - SCOPUS:85070975829
VL - 29
SP - 2642
EP - 2665
JO - International Journal of Numerical Methods for Heat and Fluid Flow
JF - International Journal of Numerical Methods for Heat and Fluid Flow
SN - 0961-5539
IS - 8
ER -