Investigation of combustion model via the local collocation technique based on moving Taylor polynomial (MTP) approximation/domain decomposition method with error analysis

authored by: Mostafa Abbaszadeh, Amirreza Khodadadian, Maryam Parvizi, Mehdi Dehghan
Abstract: In this paper, we develop a new meshless numerical procedure for simulating the combustion model. To that end, we employ a local meshless collocation method according to the moving Taylor polynomial (MTP) approximation. The space derivative is approximated by using the local approach and then the Crank–Nicolson algorithm is utilized to approximate the time derivative. The stability and convergence of the time-discrete formulation are discussed, analytically and numerically. The Broyden method is applied to solve this nonlinear system. Since the size of the physical domain is large, we employ the non-overlapping domain decomposition method (DDM) to obtain a faster numerical algorithm. The local meshless approaches are efficient numerical techniques to simulate models in the fluid flow. The obtained results show that the proposed numerical formulation has efficient results for solving this mathematical model.
Organisation(s): Institute of Applied Mathematics
External Organisation(s): Amirkabir University of Technology
Keele University
TU Wien (TUW)
Type: Article
Journal: Engineering Analysis with Boundary Elements
Volume: 159
Pages: 288-301
No. of pages: 14
ISSN: 0955-7997
Publication date: 02.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Analysis, Engineering(all), Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1016/j.enganabound.2023.11.010 (Access: Closed)

BibTeX

@article{c0b141a4d20445d3906529dd6f9787f2,
title = "Investigation of combustion model via the local collocation technique based on moving Taylor polynomial (MTP) approximation/domain decomposition method with error analysis",
abstract = "In this paper, we develop a new meshless numerical procedure for simulating the combustion model. To that end, we employ a local meshless collocation method according to the moving Taylor polynomial (MTP) approximation. The space derivative is approximated by using the local approach and then the Crank–Nicolson algorithm is utilized to approximate the time derivative. The stability and convergence of the time-discrete formulation are discussed, analytically and numerically. The Broyden method is applied to solve this nonlinear system. Since the size of the physical domain is large, we employ the non-overlapping domain decomposition method (DDM) to obtain a faster numerical algorithm. The local meshless approaches are efficient numerical techniques to simulate models in the fluid flow. The obtained results show that the proposed numerical formulation has efficient results for solving this mathematical model.",
keywords = "Broyden method, Combustion model, Computational fluid dynamic (CFD), Local meshless collocation method, Moving Taylor polynomial approximation, Stability and convergence, Water heating in home-scale heaters",
author = "Mostafa Abbaszadeh and Amirreza Khodadadian and Maryam Parvizi and Mehdi Dehghan",
note = "Funding Information: The authors are grateful to the reviewers for carefully reading this paper and for their comments and suggestions which have improved the paper. A. Khodadadian acknowledges the support by FWF (Austrian Science Fund) Standalone Project No P-36520, entitled Using Single Atom Catalysts as Nanozymes in FET Sensors FET. M. Parvizi is funded by the Alexander von Humboldt Foundation, Germany project named -matrix approximability of the inverses for FEM, BEM, and FEM-BEM coupling of the electromagnetic problems. ",
year = "2024",
month = feb,
doi = "10.1016/j.enganabound.2023.11.010",
language = "English",
volume = "159",
pages = "288--301",
journal = "Engineering Analysis with Boundary Elements",
issn = "0955-7997",
publisher = "Elsevier Ltd.",
}