Calculation of Four-Dimensional Unsteady Gas Flow via Different Quadrature Schemes and Runge-Kutta 4th Order Method

Calculation of Four-Dimensional Unsteady Gas Flow via Different Quadrature Schemes and Runge-Kutta 4th Order Method

Year:    2024

Author:    M. Salah, M. S. Matbuly, O. Civalek, Ola Ragb

Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 2 : pp. 437–458

Abstract

In this study, a (3+1) dimensional unstable gas flow system is applied and solved successfully via differential quadrature techniques based on various shape functions. The governing system of nonlinear four-dimensional unsteady Navier–Stokes equations of gas dynamics is reduced to the system of nonlinear ordinary differential equations using different quadrature techniques. Then, Runge-Kutta 4th order method is employed to solve the resulting system of equations. To obtain the solution of this equation, a MATLAB code is designed. The validity of these techniques is achieved by the comparison with the exact solution where the error reach to $≤ 1×10^{−5}.$ Also, these solutions are discussed by seven various statistical analysis. Then, a parametric analysis is presented to discuss the effect of adiabatic index parameter on the velocity, pressure, and density profiles. From these computations, it is found that Discrete singular convolution based on Regularized Shannon kernels is a stable, efficient numerical technique and its strength has been appeared in this application. Also, this technique can be able to solve higher dimensional nonlinear problems in various regions of physical and numerical sciences.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2021-0373

Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 2 : pp. 437–458

Published online:    2024-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    Statistical analysis Runge-Kutta discrete singular convolution sinc quadrature approach gas dynamics adiabatic index.

Author Details

M. Salah

M. S. Matbuly

O. Civalek

Ola Ragb

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