Dzahui

Dzahui is a library oriented to real-time simulation of ODE/PDE via Finite Element Method and OpenGL providing a simple interface.

To use it, one simply creates an .obj file (see blender and obj files) composed of triangles representing a mesh, specifies initial and/or boundary conditions:

let naviers_params = StokesParams::static_pressure().
    hydrostatic_pressure(100_f64)
    .density(1_f64)
    .force_function(
        Box::new(|_| -10_f64)
    )
    .build();

builds a window indicating the problem to solve:

let window_builder: DzahuiWindowBuilder = DzahuiWindow::builder("./assets/1dbar.obj")
    .solve_static_pressure(naviers_params)
    .with_integration_iteration(350);

let window = window_builder.build();

and runs the window:

window.run();

The resulting mesh will be colored from blue to red indicating speed (or pressure in the case of the hydrostatic pressure equation).

Available equations

• 1D time-dependent diffussion equation
• 1D time-independent diffussion equation
• Hysrostatic pressure equation (Or simplified 1D time-independent Stokes)

For now, only three equations with Dirichlet boundaries are implemented, but more will be added in the future, including two an three-dimensional cases of Navier Stokes.

How to use

Dzahui is available on crates.io. Only add it as a dependency and follow one of the many binaries available in the crate to generate a simulation.

Controls

Dzahui has a few ways to interact with the GUI: On MacOS:

• You can press esc to quit simulation
• Press s to save current result
• Hold t to view triangles of mesh
• Left-click and move mouse or trackpad to move camera

Future implementations

• Simmulate various types of curves akin to the problem being solved (like streamlines, pathlines and streaklines).
• Improve GUI by adding buttons and graphs.
• Improve method to create boundary conditions via GUI (vertex selector) and function-defined boundaries.
• Include Newmann conditions.
• Homogenize controls for view on different OS.
• Implement 2D and 3D integration algorithms.
• Improve crate structure and access modifiers.
• Improve matrix algorithms (more stable ones).
• Change/create traits to be directly implemented by the user.
• Correct some implementations to improve performance.
• Increase polynomial degree to be used on problems.
• Use macros to embed newly user-created equations into the possible equations to simmulate.

Dzahui is a project to mayor in physics at Facultad de Ciencias, UNAM.

License

MIT