pub fn resistive_diffusion_kernel(
b_manifold: &Manifold<f64, f64>,
diffusivity: Diffusivity,
) -> Result<CausalTensor<f64>, PhysicsError>Expand description
Calculates the diffusion term of the induction equation. $$ \frac{\partial \mathbf{B}}{\partial t}_{diff} = \eta \nabla^2 \mathbf{B} $$ On a manifold, this is $-\eta \Delta B$ where $\Delta = d\delta + \delta d$ is the Hodge Laplacian. Note that $\nabla^2$ in vector calc usually corresponds to $-\Delta$ (negative Laplacian). The standard diffusion eq is $\partial_t u = + D \nabla^2 u$. The Hodge Laplacian $\Delta$ is positive definite. So $\nabla^2 \approx -\Delta$. Thus $\partial_t B = - \eta \Delta B$.
§Arguments
b_manifold- Manifold containing the magnetic flux 2-form $B$.diffusivity- Magnetic diffusivity $\eta$.
§Returns
Result<CausalTensor<f64>, PhysicsError>- Rate of change tensor (2-form).