astronomix._modules._conduction._conduction

Thermal conduction for the finite-difference scheme.

We add a Fourier heat-conduction term to the energy equation,

d(rho E)/dt += div(kappa grad T) ,

with a constant conductivity kappa = params.thermal_conductivity and the temperature taken from the ideal-gas relation

T = p / rho (code units, specific gas constant R = 1).

The constant-kappa case reduces to kappa * laplacian(T) which we discretise with the standard second-order seven-point (in 3D) Laplacian. Second order is deliberate: the stencil is trivially differentiable (a constant linear operator on T) and the explicit parabolic time-step stays cheap.

Boundary conditions are adiabatic (zero conductive flux) at every wall: the reflective hydro boundary mirrors density and pressure as even quantities, so T = p / rho is mirrored too and its normal gradient – hence the conductive flux – vanishes at the wall.

Module Contents

Functions

fd_conduction_source

Conductive energy source kappa * laplacian(T) for the FD scheme.

API

astronomix._modules._conduction._conduction.fd_conduction_source(primitive_state, params, config, registered_variables)

Conductive energy source kappa * laplacian(T) for the FD scheme.

Returns a state-shaped array with only the energy slot populated; it is meant to be accumulated (times dt) onto the conserved-state RHS in the time-integrator source assembly.