Struct CoordinateTransform 

pub struct CoordinateTransform<S: Scalar> {
    pub s: S,
}

Coordinate transformation for moving boundary problems.

Maps physical domain [0, s(t)] to fixed computational domain [0, 1]. This avoids remeshing as the boundary moves.

Fields

s: S

Current boundary position

Implementations

impl<S: Scalar> CoordinateTransform<S>

pub fn new(s: S) -> Self

Create a transform for domain [0, s].

pub fn update(&mut self, s: S)

Update boundary position.

pub fn physical_to_computational(&self, x: S) -> S

Transform physical coordinate x to computational ξ. ξ = x / s(t)

pub fn computational_to_physical(&self, xi: S) -> S

Transform computational coordinate ξ to physical x. x = ξ * s(t)

pub fn jacobian(&self) -> S

Jacobian of the transform: ∂x/∂ξ = s

pub fn transform_d1(&self, du_dxi: S) -> S

Transform first derivative: ∂u/∂x = (1/s) ∂u/∂ξ

pub fn transform_d2(&self, d2u_dxi2: S) -> S

Transform second derivative: ∂²u/∂x² = (1/s²) ∂²u/∂ξ²

pub fn convection_coefficient(&self, dsdt: S, xi: S) -> S

Additional convective term from moving boundary.

When using transformed coordinates, the heat equation becomes: ∂u/∂t = α/s² ∂²u/∂ξ² + (ds/dt * ξ / s) ∂u/∂ξ

This returns the coefficient for the convective term.

Trait Implementations

impl<S: Clone + Scalar> Clone for CoordinateTransform<S>

fn clone(&self) -> CoordinateTransform<S>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.