FiniteVolumeUpwindedAdvectiveFlux

Source: models/finite_volume/FiniteVolumeUpwindedAdvectiveFlux.py

Compute upwinded advective fluxes at cell edges.

\[ J_e = v_e \, \bigl(H(v_e) u_{e^-} + (1 - H(v_e)) u_{e^+}\bigr) \]

where \(v_e\) is the cell-edge advection velocity, \(H\) is the Heaviside step (\(1\) when \(v_e > 0\), \(0\) when \(v_e < 0\)), and \(u_{e^\pm}\) are the cell-averaged values on the left (\(e^-\)) and right (\(e^+\)) of edge \(e\). The Heaviside factor selects the upwind cell – the cell from which information propagates with the velocity sign.

The chain rule uses the same upwind coefficient::

dv_coeff = H u_left + (1 - H) u_right
         = u_right + H (u_left - u_right)

so J_e = v_e * dv_coeff and d J_e / d v_e = dv_coeff.

Inputs

u — input · Scalar · required

Cell-averaged field values.

v_edge — input · Scalar · required

Cell-edge advection velocity values.

Outputs

flux — output · Scalar · required

Cell-edge advective fluxes.