Numerical Groundwater Flow Resolution

This lecture covers the numerical resolution of groundwater flows using finite differences, focusing on the discretization of Laplace's equation in 2D for steady flows. It explains the need for numerical resolution due to complex geological boundaries, heterogeneous soil nature, and transient flows. The lecture demonstrates the finite difference method with Excel, discussing the discretization of the domain, Laplace's equation, and boundary conditions. It also provides a step-by-step procedure for solving flow problems under a dam. Practical examples with Excel are shown, emphasizing the importance of interactive calculations and graphical representation of results.

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Cauchy boundary condition

In mathematics, a Cauchy (koʃi) boundary condition augments an ordinary differential equation or a partial differential equation with conditions that the solution must satisfy on the boundary; ideally so as to ensure that a unique solution exists. A Cauchy boundary condition specifies both the function value and normal derivative on the boundary of the domain. This corresponds to imposing both a Dirichlet and a Neumann boundary condition. It is named after the prolific 19th-century French mathematical analyst Augustin-Louis Cauchy.

Mixed boundary condition

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