A higher order compact scheme for the nonlinear advection diffusion processes

Murat Sari; Sufii H. Mussa; Huseyin Tunc

doi:10.29228/proc.10

A higher order compact scheme for the nonlinear advection diffusion processes

Murat Sari, Sufii H. Mussa, Huseyin Tunc

Yildiz Technical University

Research output: Contribution to journal › Article › peer-review

Abstract

This paper presents a highly accurate finite difference based scheme through the Padé approximation in analyzing the behaviour of the nonlinear advection-diffusion processes governed by the unsteady Burgers equation. It has then been proved that the present method is unconditionally stable based on the von Neumann stability analysis. The proposed approach has been shown to be capable of solving the model equation effectively. Two challenging examples have been taken to illustrate the physical behaviour of the model in detail. The computed results have been seen to be highly accurate and be oscillation free even if advection dominated cases are considered.

Original language	English
Pages (from-to)	295-310
Number of pages	16
Journal	Proceedings of the Institute of Mathematics and Mechanics
Volume	45
Issue number	2
DOIs	https://doi.org/10.29228/proc.10
Publication status	Published - 2019
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2019, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan. All rights reserved.

Keywords

Burgers equation
Compact finite difference method
Nonlinear advection diffusion process
Nonlinear modelling
Padé approximation

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10.29228/proc.10

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abstract = "This paper presents a highly accurate finite difference based scheme through the Pad{\'e} approximation in analyzing the behaviour of the nonlinear advection-diffusion processes governed by the unsteady Burgers equation. It has then been proved that the present method is unconditionally stable based on the von Neumann stability analysis. The proposed approach has been shown to be capable of solving the model equation effectively. Two challenging examples have been taken to illustrate the physical behaviour of the model in detail. The computed results have been seen to be highly accurate and be oscillation free even if advection dominated cases are considered.",

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AU - Mussa, Sufii H.

AU - Tunc, Huseyin

PY - 2019

Y1 - 2019

N2 - This paper presents a highly accurate finite difference based scheme through the Padé approximation in analyzing the behaviour of the nonlinear advection-diffusion processes governed by the unsteady Burgers equation. It has then been proved that the present method is unconditionally stable based on the von Neumann stability analysis. The proposed approach has been shown to be capable of solving the model equation effectively. Two challenging examples have been taken to illustrate the physical behaviour of the model in detail. The computed results have been seen to be highly accurate and be oscillation free even if advection dominated cases are considered.

AB - This paper presents a highly accurate finite difference based scheme through the Padé approximation in analyzing the behaviour of the nonlinear advection-diffusion processes governed by the unsteady Burgers equation. It has then been proved that the present method is unconditionally stable based on the von Neumann stability analysis. The proposed approach has been shown to be capable of solving the model equation effectively. Two challenging examples have been taken to illustrate the physical behaviour of the model in detail. The computed results have been seen to be highly accurate and be oscillation free even if advection dominated cases are considered.

KW - Burgers equation

KW - Compact finite difference method

KW - Nonlinear advection diffusion process

KW - Nonlinear modelling

KW - Padé approximation

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JO - Proceedings of the Institute of Mathematics and Mechanics

JF - Proceedings of the Institute of Mathematics and Mechanics

IS - 2

ER -

A higher order compact scheme for the nonlinear advection diffusion processes

Abstract

Bibliographical note

Keywords

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