Struct StefanProblem 

pub struct StefanProblem {
    pub n: usize,
    pub dx: f64,
    pub temperature: Vec<f64>,
    pub interface_pos: f64,
    pub latent_heat: f64,
    pub stefan_number: f64,
    /* private fields */
}

1D Stefan problem: solidification with a moving solid-liquid interface.

The domain [0, L] contains two phases separated by a sharp interface at position s(t). In each phase the temperature satisfies the heat equation, and the interface velocity is determined by the Stefan condition (energy balance).

Model

∂T/∂t = α ∂²T/∂x²  (uniform thermal diffusivity α = 1)
Interface:  ρ L ds/dt = -[k ∂T/∂n]  (latent heat release)
Stefan condition simplified: ds/dt = (T_x|_s⁺ - T_x|_s⁻) / St

The implementation uses a fixed-grid enthalpy method with a smoothed interface to avoid explicit front tracking.

Fields

n: usize

Number of grid points

dx: f64

Grid spacing

temperature: Vec<f64>

Temperature field T(x)

interface_pos: f64

Current interface position s (lattice coordinate)

latent_heat: f64

Latent heat L

stefan_number: f64

Stefan number St = c_p * ΔT / L

Implementations

impl StefanProblem

pub fn new( n: usize, l: f64, initial_interface: f64, latent_heat: f64, stefan_number: f64, ) -> IntegrateResult<Self>

Create a new Stefan problem.

Arguments

• n — number of grid points
• l — domain length
• initial_interface — starting interface position ∈ (0, l)
• latent_heat — latent heat L (energy/volume)
• stefan_number — Stefan number St = c_p ΔT / L

pub fn step(&mut self, dt: f64)

Advance the Stefan problem by one time step using an explicit method.

Uses the enthalpy-based update where interface motion is recovered from the Stefan condition applied at the nearest grid cell to the interface.

pub fn run(&mut self, t_final: f64, dt: f64) -> Vec<(f64, f64)>

Run the Stefan problem and return the time history of (time, interface_position).

The interface position is returned in physical coordinates (metres).

pub fn interface_position_phys(&self) -> f64

Return the current interface position in physical coordinates.

pub fn stefan_number(&self) -> f64

Return the Stefan number.