Simulations of nonlinear advection-diffusion models through various finite element techniques

H. Tunc, M. Sari*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

In this study, the Burgers equation is analyzed both numerically and mathematically by considering various finite element based techniques including Galerkin, Taylor-Galerkin and collocation methods for spatial variation of the equation. The obtained time dependent ordinary differential equation system is approximately solved by ff-family of time approximation. All these methods are theoretically explained using cubic B-spline basis and weight functions for a strong form of the model equation. Von Neumann matrix stability analysis is performed for each of these methods and stability criteria are determined in terms of the problem parameters. Some challenging examples of the Burgers equation are numerically solved and compared with the literature and exact solutions. Also, the proposed techniques have been compared with each other in terms of their advantages and disadvantages depending on the problem types. The more advantageous method of the three, in comparison to the other two, has been found for the special cases of the present problem in detail.

Original languageEnglish
Pages (from-to)2853-2870
Number of pages18
JournalScientia Iranica
Volume27
Issue number6 B
DOIs
Publication statusPublished - Nov 2020
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2020 Sharif University of Technology. All rights reserved.

Funding

The rst author would like to thank the Science Fellowships and Grant Programmes Department of TUBITAK (TUBITAK BIDEB) for their support of this academic research.

FundersFunder number
Programmes Department of TUBITAK
TUBITAK BIDEB

    Keywords

    • Advection-diffusion model
    • Burgers equation
    • Collocation method
    • Ff-family of approximation
    • Finite element method
    • Taylor-Galerkin method

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