An enhanced SUPG-stabilized finite element formulation for simulating natural phenomena governed by coupled system of reaction-convection-diffusion equations

Süleyman Cengizci

doi:10.53391/mmnsa.1387125

EN

An enhanced SUPG-stabilized finite element formulation for simulating natural phenomena governed by coupled system of reaction-convection-diffusion equations

Abstract

Many phenomena arising in nature, science, and industry can be modeled by a coupled system of reaction-convection-diffusion (RCD) equations. Unfortunately, obtaining analytical solutions to RCD systems is typically not possible and, therefore, usually requires the use of numerical methods. On the other hand, since solutions to RCD-type equations can exhibit rapid changes and may have boundary/inner layers, classical computational tools yield approximations polluted with physically meaningless oscillations when convection dominates the transport process. Towards that end, in order to eliminate such numerical instabilities without sacrificing accuracy, this work employs a stabilized finite element formulation, the so-called streamline-upwind/Petrov-Galerkin (SUPG) method. The SUPG-stabilized formulation is then also supplemented with the YZ$\beta$ shock-capturing mechanism to achieve higher-quality approximations around sharp gradients. A comprehensive set of numerical test experiments, including cross-diffusion systems, the Schnakenberg reaction model, and mussel-algae interactions, is considered to reveal the robustness of the proposed formulation, which we call the SUPG-YZ$\beta$ formulation. Comparisons with reported studies reveal that the proposed formulation performs quite well without introducing excessive numerical dissipation.

Keywords

Reaction-convection-diffusion, finite elements, stabilization, shock-capturing, SUPG-YZ$\beta$ formulation

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Details

Primary Language

English

Subjects

Finite Element Analysis , Numerical and Computational Mathematics (Other)

Journal Section

Research Article

Authors

Süleyman Cengizci ^*
0000-0002-4345-1253
Türkiye

Publication Date

December 30, 2023

Submission Date

November 6, 2023

Acceptance Date

December 9, 2023

Published in Issue

Year 2023 Volume: 3 Number: 4

DOI

https://doi.org/10.53391/mmnsa.1387125

IZ

https://izlik.org/JA86ET26ST

APA

Cengizci, S. (2023). An enhanced SUPG-stabilized finite element formulation for simulating natural phenomena governed by coupled system of reaction-convection-diffusion equations. Mathematical Modelling and Numerical Simulation With Applications, 3(4), 297-317. https://doi.org/10.53391/mmnsa.1387125

AMA

1.Cengizci S. An enhanced SUPG-stabilized finite element formulation for simulating natural phenomena governed by coupled system of reaction-convection-diffusion equations. MMNSA. 2023;3(4):297-317. doi:10.53391/mmnsa.1387125

Chicago

Cengizci, Süleyman. 2023. “An Enhanced SUPG-Stabilized Finite Element Formulation for Simulating Natural Phenomena Governed by Coupled System of Reaction-Convection-Diffusion Equations”. Mathematical Modelling and Numerical Simulation With Applications 3 (4): 297-317. https://doi.org/10.53391/mmnsa.1387125.

EndNote

Cengizci S (December 1, 2023) An enhanced SUPG-stabilized finite element formulation for simulating natural phenomena governed by coupled system of reaction-convection-diffusion equations. Mathematical Modelling and Numerical Simulation with Applications 3 4 297–317.

IEEE

[1]S. Cengizci, “An enhanced SUPG-stabilized finite element formulation for simulating natural phenomena governed by coupled system of reaction-convection-diffusion equations”, MMNSA, vol. 3, no. 4, pp. 297–317, Dec. 2023, doi: 10.53391/mmnsa.1387125.

ISNAD

Cengizci, Süleyman. “An Enhanced SUPG-Stabilized Finite Element Formulation for Simulating Natural Phenomena Governed by Coupled System of Reaction-Convection-Diffusion Equations”. Mathematical Modelling and Numerical Simulation with Applications 3/4 (December 1, 2023): 297-317. https://doi.org/10.53391/mmnsa.1387125.

JAMA

1.Cengizci S. An enhanced SUPG-stabilized finite element formulation for simulating natural phenomena governed by coupled system of reaction-convection-diffusion equations. MMNSA. 2023;3:297–317.

MLA

Cengizci, Süleyman. “An Enhanced SUPG-Stabilized Finite Element Formulation for Simulating Natural Phenomena Governed by Coupled System of Reaction-Convection-Diffusion Equations”. Mathematical Modelling and Numerical Simulation With Applications, vol. 3, no. 4, Dec. 2023, pp. 297-1, doi:10.53391/mmnsa.1387125.

Vancouver

1.Süleyman Cengizci. An enhanced SUPG-stabilized finite element formulation for simulating natural phenomena governed by coupled system of reaction-convection-diffusion equations. MMNSA. 2023 Dec. 1;3(4):297-31. doi:10.53391/mmnsa.1387125