Numerical solution of the heat advection equation in a two-dimensional domain using the discontinuous Galerkin method

• Autorzy: Węgrzyn-Skrzypczak Ewa

Identyfikatory

DOI

10.17512/jamcm.2023.3.05

• Języki publikacji: EN

Abstrakty

EN

This paper presents a numerical solution of the heat advection equation in a two dimensional domain using the Discontinuous Galerkin Method (DGM). The advection equation is widely used in heat transfer problems, particularly in the field of fluid dynamics. The discontinuous Galerkin method is a numerical technique that allows for the solution of partial differential equations using a piecewise polynomial approximation. In this study, DGM is applied to the heat advection equation and its effectiveness in solving the problem is investigated. The findings of this study suggest that the Discontinuous Galerkin Method is a promising approach for solving heat transfer problems in a two-dimensional domain.

Słowa kluczowe

EN

heat advection equation; discontinuous Galerkin method; heat transfer problem; computational methods

PL

równanie adwekcji ciepła; nieciągła metoda Galerkina; wymiana ciepła; metody obliczeniowe

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2023
• Tom: Vol. 22, nr 3
• Strony: 57--68
• Opis fizyczny: Bibliogr. 12 poz., rys., tab.

Twórcy

autor

Węgrzyn-Skrzypczak Ewa

• Department of Mathematics, Czestochowa University of Technology, Czestochowa, Poland

Bibliografia

• [1] Dimov, I., Farago, I., & Vulkov, L. (2015). Finite Difference Methods, Theory and Applications. Springer-Verlag GmbH.
• [2] Whiteley, J. (2017). Finite Element Methods: A Practical Guide. Springer Int. Pub. AG.
• [3] Maliska, C. (2023). The Finite Volume Method. DOI: 10.1007/978-3-031-18235-8.3.
• [4] Reed, W.H., & Hill, T.R. (1973). Triangular Mesh Methods for the Neutron Transport Equation. Technical report LA-UR-73-479, Los Alamos National Laboratory. Los Alamos.
• [5] Lesaint, P., & Raviart, A. (1974). On a Finite Element Method for Solving the Neutron Transport Equation, in: Mathematical Aspects of Finite Elements in Partial Differential Equations. C.A. deBoor. New York: Academic Press, 89-123.
• [6] Dolejší, V., & Feistauer, M. (2015). Discontinuous Galerkin Method: Analysis and Applications to Compressible Flow. Cham: Springer.
• [7] Pozorski, Z., & Pozorska, J. (2022). Influence of the heterogeneity of the core material on the local instability of a sandwich panel. Materials 2022, 15(19), 6687. DOI: 10.3390/ma15196687
• [8] Pozorska, J. (2018). Numerical modelling of sandwich panels with a non-continuous soft core. MATEC Web Conf., 157, 06007. DOI: 10.1051/matecconf/201815706007
• [9] LeVeque, R.J. (2012). Finite Volume Methods for Hyperbolic Problems. Cambridge University Press.
• [10] Flaherty, J.E., Krivodonova, L., Remacle, J.-F., & Shephard, M.S. (2002), Aspects of discontinuous Galerkin methods for hyperbolic conservation laws. Element Analysis and Design, 38(10), 889-908.
• [11] Chandrasekar, A. (2022), Numerical Methods for Atmospheric and Oceanic Sciences. Cambridge University Press.
• [12] Koornwinder, T.H. (1984). Orthogonal polynomials with weight function (1-x)α(1+x)β+Mδ(x+1)+ Nδ(x-1). Canadian Mathematical Bulletin, 27(2), 205-214.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).