sandbox/haouche/README

    My Sandbox

    Welcome to the README for my sandbox! I’m a PhD student passionate about numerical methods — so if you’re like me, just enjoy :)

    Here, you’ll explore the numerical techniques behind fluid simulations and see why Basilisk is such a WONDERFUL tool. I’ll walk you through some classical examples in fluid mechanics and show how numerical methods bring them to life.

    Whether you’re a beginner or an enthusiast, I hope you find something useful or inspiring here.

    Just below, you’ll see a beautiful channel…

    -Ilies Haouche-

    YouTube Channel

    You can just click on my head YouTub Channel or here :)

    So if you’re into fluid mechanics and love simulations, check out my YouTube channel — I share hands-on tutorials on Basilisk and the physics behind real fluid flows.

    Numerical methods course

    This section summarizes key numerical techniques used in scientific computing, particularly for solving partial differential equations (PDEs). The focus is on two core approaches: finite difference methods (FDM) and finite volume methods (FVM).

    • Finite Difference Methods involve approximating derivatives by using differences between values at discrete grid points. They are intuitive, easy to implement, and suitable for structured grids. FDM is commonly used in early-stage teaching or in problems with regular geometries.

    • Finite Volume Methods, in contrast, are based on the integral form of the conservation laws. They ensure local conservation of physical quantities and are especially suited for complex geometries and unstructured meshes. FVM is widely used in computational fluid dynamics (CFD) and is the method adopted in Basilisk.

    This module includes short notes, examples, and code snippets to illustrate these methods and how they relate to real simulations.

    Finite difference methods [FDM]

    Finite volume methods [FVM]

    Physical cases

    This section presents various physical mechanisms commonly encountered in fluid dynamics, with a focus on real-world effects that go beyond pure numerical methods.

    • Hydrodynamic instabilities, such as Rayleigh–Taylor and Kelvin–Helmholtz, which arise due to density differences and shear in stratified flows…
    • Surfactants and Marangoni effects, which influence interfacial tension and drive flows due to surface tension gradients.
    • Multiphase flows, where interactions between different fluid phases lead to rich and complex behaviors.

    These cases combine physics and numerical modeling to better understand fluid systems under realistic conditions.

    Hydrodynamic instabilities

    Other examples

    Soluble surfactants

    Post-processing

    MPI

    Contact

    If you like to discuss a specific topic, feel free to e-mail me: ilies.haouche2000@gmail.com.