Flow past a cylinder¶

use ironlab::prelude::*;

use crate::fields::*;

pub const TITLE: &str = "Flow past a cylinder";
pub const DESCRIPTION: &str = "The speed of the potential flow past a circular cylinder, drawn as a surface in a \
     two-dimensional axes on a polar mesh whose rings crowd towards the cylinder. A surface in a two-dimensional axes \
     is seen from directly above, which makes it the pseudocolour plot of MATLAB's `pcolor`: the field values belong \
     to the vertices of the mesh, so the mesh may be curvilinear, which the pixels of an image cannot be.";

/// The number of rings of the mesh, from the surface of the cylinder to the outer radius.
const RINGS: usize = 17;

/// The number of spokes of the mesh; the first and the last coincide, which closes the mesh round the cylinder.
const SPOKES: usize = 73;

/// The radius of the outermost ring, in cylinder radii.
const OUTER_RADIUS: f64 = 4.0;

pub fn figure() -> Figure {
    // Matrices of coordinates, rather than vectors, give every vertex its own position.
    let (x, y, speed) = cylinder_flow_mesh(RINGS, SPOKES, OUTER_RADIUS);

    let mut fig = Figure::new()
        .size_mm(120.0, 124.0)
        .title(r"Speed $|\mathbf{u}| / U_\infty$ of the potential flow past a cylinder");
    let mut ax = fig.axes(0, 0);
    // `surface` leaves the axes two-dimensional, where `surf` would convert it to three dimensions.
    ax.surface(x, y, &speed).edge_width(0.25);
    ax.colormap(Colormap::Viridis)
        .xlabel("$x / a$")
        .ylabel("$y / a$");
    fig
}