PLUTO Test Problems  4.4-patch2
init.c File Reference

Shadow test. More...

Detailed Description

Sets up a 2D problem in which a free-streaming radiation field encounters a highly opaque region of space, casting a shadow behind it.

A constant density $ \rho_0 $ is fixed in the whole space, except in an elliptic region around the coordinate origin where $ \rho=\rho_1\gg\rho_0 $. In order to have a smooth transition between $\rho_0$ and $\rho_1$, the initial density field is defined as

\[ \rho\,(x,y)=\rho_0 + \frac{\rho_1-\rho_0}{1+e^\Delta}\,, \]

where $\Delta=10 \left[ \left(\frac{x}{x_0}\right)^2 + \left(\frac{y}{y_0}\right)^2 -1 \right]$. Initially, matter is set in thermal equilibrium with radiation at a temperature $T_0$, and fluxes and velocities are initialized to zero. Radiation is injected from the left boundary at a temperature $T_1>T_0$, with a flux $\mathbf{F}_r=E_r\,\hat{\mathbf{e}}_x$.

In all configurations scattering is neglected, while the absorption opacity is set as constant in Configuration #1, and according to Kramers' law, i.e., $\kappa=\kappa_0\left(\frac{\rho}{\rho_0}\right) \left(\frac{T}{T_0}\right)^{-3.5}$, in Configurations #2 and #3.

Only the upper half of the elliptic region is described in Configurations #1 and #3, where reflective boundary conditions have been imposed at the bottom boundary. Conversely, the entire elliptic region is described in Configuration #2, where outflow conditions are imposed in all boundaries but the left one. AMR can be applied to Configuration #3, where cells are tagged for refinement for large values of the second derivative of $\rho/\rho_0+E_r/a_RT_1^4$.

Author
J. D. Melon Fuksman (fuksm.nosp@m.an@m.nosp@m.pia.d.nosp@m.e)
Date
Dec 12, 2019

References