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

General independent paramters:

• Density at infinity \(\rho_\infty\)
• Temperature at infinity \(T_\infty\)
• Constant opacity \(\kappa\)
• Adiabatic constant \(\gamma\)
• Central mass \(M\)
• molecular Mass of gas molecules \(m_\text{molec}\)

Useful dependent parameters:

• Sound velocity:

\[c_\text{s} = \sqrt{\frac{T \gamma k_\text{B}}{m_\text{molec}}}\]

• Bondi Radius:

\[r_\text{B} = \frac{GM}{2c_{\text{s},\infty}^2} = \frac{GM m_\text{molec}}{2T\gamma k_\text{B}}\]

Parameters for belt:

• Central Mass:

\[M = M_\odot\]

• Optical density:

\[\kappa = \]

• Adiabatic constant/degrees of freedom

\[\gamma = \frac{7}{5} \rightarrow \text{degrees of freedom} = 5\]

• inner radius:

\[r_\text{s} = 10^{-2} r_B\]

• outer radius:

\[r_\text{s} = 10^{-2} r_B\]

• molecular mass:

\[m_\text{molec} = \]

Boundary conditions for fields in belt...

...at outer radius \(r_\text{o}\):

\[ p(r_\text{o}) = \frac{\rho_\infty k_\text{b} T_\infty}{m_\text{molec}}\]

\[ \rho (r_\text{o}) = \rho_\infty\]

\[\partial_r v(r_\text{o}) = 0\]

\[E_\text{r}(r_\text{o}) = a_\text{r} T_\infty^4\]

...at inner radius \(r_\text{s}\):

\[\partial_r p(r_\text{s}) = 0\]

\[\partial_r \rho (r_\text{s}) = 0\]

\[\partial_r v(r_\text{s}) = 0\]

\[\partial_r E_\text{r}(r_\text{s}) = 0\]

(While the zero gradient conditions do not match theoretical curves they should still be appropriate as the will only lead to local devastationdeviations near the respective boundary.)

Code-Anpassungen...

(Lothar)

für konstante Zentralmasse

• 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

für Dirichlet-RBn

Abgesehen von reflective zur Nullsetzung der Normalkomponenten von \(\vec v\) und \(\vec B\) bietet PLUTO keine Dirichlet-RBn. Workaround:

• gewünschte Randwerte in Init() oder InitDomain() in den Geisterzellen (Zellen mit il<IBEG bzw. il>IEND) setzen
• Wahl userdef in pluto.ini, aber in UserDefBoundary() am entsprechenden Rand gar keine Manipulationen vornehmen

aktuelle Probleme

Run wirft Fehler mit folgendem Output im Terminal:

###   ... Initialize Profiling ...                                           ###
###       prof[ 0]: Main Loop
###       prof[ 1]: Magneto-Hydrodynamics / Self-Gravity / Haumea
###       prof[ 2]: Self-Gravity / Haumea
###       prof[ 3]: Radiation / Makemake
###       prof[ 4]: Ionization / Sedna
###       prof[ 5]: Stellar Evolution
###       prof[ 6]: Dust Evolution
###       prof[ 7]: CAK Line Acceleration
###       prof[ 8]: I/O
###       prof[ 9]: Radiation - Irradiation
###       prof[10]: Radiation - FLD
###       prof[11]: Radiation - UpdateDustTemperature
! ParamFileGet(): label '10.0
' was not found
[elias-HP-Pavilion-Laptop-15-cw1xxx:21078] *** Process received signal ***
[elias-HP-Pavilion-Laptop-15-cw1xxx:21078] Signal: Segmentation fault (11)
[elias-HP-Pavilion-Laptop-15-cw1xxx:21078] Signal code: Address not mapped (1)
[elias-HP-Pavilion-Laptop-15-cw1xxx:21078] Failing at address: 0xc0
[elias-HP-Pavilion-Laptop-15-cw1xxx:21078] [ 0] /usr/lib/x86_64-linux-gnu/libc.so.6(+0x45cb0) [0x7ae2c8c45cb0]
[elias-HP-Pavilion-Laptop-15-cw1xxx:21078] [ 1] /usr/lib/x86_64-linux-gnu/libc.so.6(+0x707c5) [0x7ae2c8c707c5]
[elias-HP-Pavilion-Laptop-15-cw1xxx:21078] [ 2] ./belt(+0x1a0ea) [0x5ef72f2440ea]
[elias-HP-Pavilion-Laptop-15-cw1xxx:21078] [ 3] ./belt(+0x146aa) [0x5ef72f23e6aa]
[elias-HP-Pavilion-Laptop-15-cw1xxx:21078] [ 4] ./belt(+0x1d725) [0x5ef72f247725]
[elias-HP-Pavilion-Laptop-15-cw1xxx:21078] [ 5] ./belt(+0xcff9) [0x5ef72f236ff9]
[elias-HP-Pavilion-Laptop-15-cw1xxx:21078] [ 6] /usr/lib/x86_64-linux-gnu/libc.so.6(+0x2a601) [0x7ae2c8c2a601]
[elias-HP-Pavilion-Laptop-15-cw1xxx:21078] [ 7] /usr/lib/x86_64-linux-gnu/libc.so.6(__libc_start_main+0x88) [0x7ae2c8c2a718]
[elias-HP-Pavilion-Laptop-15-cw1xxx:21078] [ 8] ./belt(+0xe015) [0x5ef72f238015]
[elias-HP-Pavilion-Laptop-15-cw1xxx:21078] *** End of error message ***

Was könnte den segmentation fault verursachen?