Numerical Solutions of Potential Flow Equations using Finite Differences

Lucy Annastacia; Collins Andete; Collins Wanyama; Paul Yongo; Benjamin Mwendwa; Griffin Omondi

doi:10.51867/Asarev.Maths.1.1.5

Authors

Lucy Annastacia Department of Mathematics, Masinde Muliro University of Science and Technology, P. O. Box 190-50100, Kakamega, Kenya. Author
Collins Andete Department of Mathematics, Masinde Muliro University of Science and Technology, P. O. Box 190-50100, Kakamega, Kenya. Author
Collins Wanyama Department of Mathematics, Masinde Muliro University of Science and Technology, P. O. Box 190-50100, Kakamega, Kenya Author
Paul Yongo Department of Mathematics, Masinde Muliro University of Science and Technology, P. O. Box 190-50100, Kakamega, Kenya. Author
Benjamin Mwendwa Department of Mathematics, Masinde Muliro University of Science and Technology, P. O. Box 190-50100, Kakamega, Kenya. Author
Griffin Omondi Department of Mathematics, Masinde Muliro University of Science and Technology, P. O. Box 190-50100, Kakamega, Kenya. Author

DOI:

https://doi.org/10.51867/Asarev.Maths.1.1.5

Keywords:

Computational Tool, Fluid Dynamics, Potential Flow Equations

Abstract

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.

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