Finite Difference Discretization of Third-Order Advection Water Seepage Equation in Earth Dams

• Author(s): Moses Kalibo Nyongesa ; Vincent Marani ; Michael Oduor Okoya
• Paper ID: 1709953
• Page: 1-5
• Published Date: 06-08-2025
• Published In: Iconic Research And Engineering Journals
• Publisher: IRE Journals
• e-ISSN: 2456-8880
• Volume/Issue: Volume 9 Issue 2 August-2025

Abstract

This paper presents the finite difference discretization of a third-order advection water seepage equation for earth dam analysis. Traditional seepage models have predominantly focused on diffusion-dominated transport, systematically neglecting advection effects that may be significant in heterogeneous dam materials. This study develops a comprehensive mathematical framework for discretizing the enhanced seepage equation: ?u/?t = ?(?u/?x) + ?(?²u/?x²) + ?(?³u/?x²?t) + f(x), where the advection term ?(?u/?x) represents bulk transport mechanisms previously omitted in seepage analysis. Using Taylor series expansion methodology, finite difference approximations are systematically developed for each differential operator. The discretization process transforms the continuous partial differential equation into a computationally tractable algebraic system, enabling numerical solution implementation. The resulting Crank-Nicolson finite difference scheme demonstrates second-order spatial accuracy and first-order temporal accuracy. This discretization framework provides the foundation for comprehensive seepage analysis that incorporates both diffusive and advective transport mechanisms, offering enhanced accuracy for dam safety assessment compared to traditional diffusion-only models.

Keywords

Finite Difference Method, Seepage Equation, Earth Dams, Advection-Diffusion

Citations

IRE Journals:
Moses Kalibo Nyongesa , Vincent Marani , Michael Oduor Okoya "Finite Difference Discretization of Third-Order Advection Water Seepage Equation in Earth Dams" Iconic Research And Engineering Journals Volume 9 Issue 2 2025 Page 1-5

IEEE:
Moses Kalibo Nyongesa , Vincent Marani , Michael Oduor Okoya "Finite Difference Discretization of Third-Order Advection Water Seepage Equation in Earth Dams" Iconic Research And Engineering Journals, 9(2)