Numerical Solutions of Potential Flow Equations using Finite Differences
DOI:
https://doi.org/10.51867/Asarev.Maths.1.1.5Keywords:
Computational Tool, Fluid Dynamics, Potential Flow EquationsAbstract
This article delves into the numerical solutions of potential flow equations using finite differences, aiming to enhance our understanding of fluid dynamics. The general objective is to obtain numerical solutions to potential flow equations using finite differences, with specific objectives including the investigation of potential flow equations, the solutions of associated PDE and the analysis of the stability of employed numerical schemes. The study employs a combination of numerical methods to achieve its objectives; MATLAB is utilized as a computational tool, while the Gauss-Seidel and Jacobi’s iterative methods are implemented for solving PDEs. Central differences are employed for discretization. The study yields valuable insights into the behaviour of potential flow systems. The significance of this research lies in its contribution to advancing our comprehension of fluid dynamics with potential applications. Generally, this work provides a foundation for further exploration and application of numerical methods in the study of potential flow.
References
A˚ke Bjo¨rck. Numerical Methods for Least Squares Problems. SIAM, Philadelphia, 1996. DOI: https://doi.org/10.1137/1.9781611971484
C.Hirseh. Numerical Computation of Internal and External Flows (VOL2). New York:John Wiley Sons,1994.
David H. Bailey, Karthik Jeyabalan, and Xiaoye S. Li. A Comparison of Three High-Precision Quadrature Schemes. Experimental Mathematics, 14(3):317-329, January 2005. https://doi.org/10.1080/10586458.2005.10128931 DOI: https://doi.org/10.1080/10586458.2005.10128931
E. Ward Cheney and David R. Kincaid. Numerical Mathematics and Computing. Cengage Learning, May 2012.
Faber, T.E. Fluid Dynamics for Physicists. New York: Cambridge University Press, 1995.
https://doi.org/10.1017/CBO9780511806735 DOI: https://doi.org/10.1017/CBO9780511806735
Jared L. Aurentz, Thomas Mach, Raf Vandebril, and David S. Watkins. Fast and Backward Stable Computation of Roots of Polynomials. SIAM Journal on Matrix Analysis and Applications, 36(3):942-973, January 2015. https://doi.org/10.1137/140983434 DOI: https://doi.org/10.1137/140983434
Kathryn E. Brenan, S. L. Campbell, and Linda R. Petzold. Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. Number 14 in Classics in Applied Mathematics. Society for Industrial and Applied Mathematics, Philadelphia, 1996. https://doi.org/10.1137/1.9781611971224 DOI: https://doi.org/10.1137/1.9781611971224
Kendall E. Atkinson. An Introduction to Numerical Analysis. Wiley, New York, 2nd ed edition, 1989.
Lamb, S.H. Hydrodynamics, 6th ed. New York: Dover, 1945.
Lighthill, M.J.S. An Informal Introduction to Theoretical Fluid Mechanics. Oxford, England: Oxford University Press, 1986.
Meyer, R.E. Introduction to Mathematical Fluid Dynamics. New York: Dover, 1982.
Patterson, A.R. A First Course in Fluid Dynamics. Cambridge University Press 1983 (1992 printing).
Sabersky, R.H.; Acosta, A.J.; Hauptmann, E.G. Fluid Flow: A First Course in Fluid Mechanics, 3rd ed. New York: Macmillan Publishing Company, 1989.
Stoker, J.J. Water waves: the mathematical theory with applications. New York: Interscience Publishers, 1957.
S. M. Baer and T. Erneux. Singular Hopf Bifurcation to Relaxation Oscillations. SIAM Journal on Applied Mathematics, 46(5):721-739, October 1986. https://doi.org/10.1137/0146047 DOI: https://doi.org/10.1137/0146047
Downloads
Published
Issue
Section
License
Copyright (c) 2024 Lucy Annastacia, Collins Andete, Collins Wanyama, Paul Yongo, Benjamin Mwendwa, Griffin Omondi (Author)
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.