BA Elias Saarmann

• Diss auf Overleaf

Literature

• Radiating Bondi Flows I
• PLUTO manual

Bondary Conditions

in Radiating Bondi Flows I

For the outer boundry conditions \(r \rightarrow \infty\) \[ (\tilde{\rho},\mathcal{M}, s, \tilde{L}, \tilde{E}_\text{r}) \rightarrow (1, 0, s_\infty, \tilde{L}_\infty, 1) \]

With dimensionless density \( \tilde{\rho} = \frac{\rho(r)}{\rho_\infty}\), Mach number \(\mathcal{M} = \frac{v(r)}{c_s(r)}\), dimensionless entropy \( s = \frac{S}{c_\text{V}}\) and dimensionless radiation Energy density \(\tilde{E}_\text{r} = \frac{E_\text{r}}{a_\text{r}T_\infty^4}\).

in PLUTO/belt

Adiabatic constant \(\gamma\).

This determines the equation of state

\[

T = \frac{m_\text{molec} c_\text{s}^2}{\gamma k_\text{B}}\,.

\]

Enforce constant optical density \(\kappa\).

Constant central mass \(M\).

Temperature at outer radius \(T_\infty\).

This determines radiation energy density at outer radius.

\[

E_{\text{r},\infty} = a_\text{r} T_\infty^4

\]

Both \(T\) and \(E_\text{r}\) should be zero-gradient at infinity.

Zero gradient boundary conditions should be generally appropriate and will likely only lead to local deviations from theoretical curves near the boundaries.

Code-Anpassungen für konstante Zentralmasse

(Lothar)

• M_centr (o.Ä.) als weiteren Parameter in user_defined_parameters.h definieren und die Anzahl USER_DEF_PARAMETERS entsprechend erhöhen
• den Wert von M_centr in pluto.ini unter [Parameters] setzen (in Gramm)
• body-force.c aus belt/src/Misc in den Run-Folder kopieren und in Zeile 64 die M_X1_BEG durch (g_inputParam[M_centr]/ReferenceMass) ersetzen