BA Elias Saarmann: Difference between revisions
(Expanded section for simulation boundary conditions to be more complete.) |
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== in PLUTO/belt == | == 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: | |||
Sound velocity: | |||
<nowiki>\[c_\text{s} = \sqrt{\frac{T \gamma k_\text{B}}{m_\text{molec}}}\]</nowiki> | <nowiki>\[c_\text{s} = \sqrt{\frac{T \gamma k_\text{B}}{m_\text{molec}}}\]</nowiki> | ||
Bondi Radius: | * Bondi Radius: | ||
<nowiki>\[r_\text{B} = \frac{GM}{2c_{\text{s},\infty}^2 = \frac{GM m_\text{molec}}{2T\gamma k_\text{B | <nowiki>\[r_\text{B} = \frac{GM}{2c_{\text{s},\infty}^2} = \frac{GM m_\text{molec}}{2T\gamma k_\text{B}}\]</nowiki> | ||
Parameters for belt: | === Parameters for belt: === | ||
Central Mass: | * Central Mass: | ||
\[M = M_\odot\] | \[M = M_\odot\] | ||
Optical density: | * Optical density: | ||
\[\kappa = \] | \[\kappa = \] | ||
Adiabatic constant/degrees of freedom | * Adiabatic constant/degrees of freedom | ||
\[gamma = \frac{7}{5} \rightarrow \text{degrees of freedom} = 5\] | \[\gamma = \frac{7}{5} \rightarrow \text{degrees of freedom} = 5\] | ||
inner radius: | * inner radius: | ||
\[r_\text{s} = 10^{-2} r_B\] | \[r_\text{s} = 10^{-2} r_B\] | ||
outer radius: | * outer radius: | ||
\[r_\text{s} = 10^{-2} r_B\] | \[r_\text{s} = 10^{-2} r_B\] | ||
molecular mass: | * molecular mass: | ||
\[m_\text{molec} = \] | \[m_\text{molec} = \] | ||
Boundary conditions for fields in belt... | === Boundary conditions for fields in belt... === | ||
...at outer radius \(r_\text{o}\): | ==== ...at outer radius \(r_\text{o}\): ==== | ||
<nowiki>\[ p(r_\text{o}) = \frac{\rho_\infty k_\text{b} T_\infty}{m_\text{molec}}\]</nowiki> | <nowiki>\[ p(r_\text{o}) = \frac{\rho_\infty k_\text{b} T_\infty}{m_\text{molec}}\]</nowiki> | ||
\[ \rho (r_\text{o}) = rho_\infty\] | \[ \rho (r_\text{o}) = \rho_\infty\] | ||
\[\partial_r v(r_\text{o}) = 0\] | \[\partial_r v(r_\text{o}) = 0\] | ||
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\[E_\text{r}(r_\text{o}) = a_\text{r} T_\infty^4\] | \[E_\text{r}(r_\text{o}) = a_\text{r} T_\infty^4\] | ||
...at inner radius \(r_\ | ==== ...at inner radius \(r_\text{s}\): ==== | ||
\[\partial_r p(r_\text{s}) = 0\] | \[\partial_r p(r_\text{s}) = 0\] | ||
| Line 93: | Line 86: | ||
\[\partial_r E_\text{r}(r_\text{s}) = 0\] | \[\partial_r E_\text{r}(r_\text{s}) = 0\] | ||
(While the zero gradient conditions do not match theoretical curves they should still be appropriate as the will only lead to local devastation near the respective boundary.) | (While the zero gradient conditions do not match theoretical curves they should still be appropriate as the will only lead to local <s>devastation</s>deviations near the respective boundary.) | ||
= Code-Anpassungen für konstante Zentralmasse = | = Code-Anpassungen für konstante Zentralmasse = | ||
Latest revision as of 09:58, 2 July 2026
Literature
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 für konstante Zentralmasse
(Lothar)
M_centr(o.Ä.) als weiteren Parameter in user_defined_parameters.h definieren und die AnzahlUSER_DEF_PARAMETERSentsprechend erhöhen- den Wert von
M_centrin 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_BEGdurch(g_inputParam[M_centr]/ReferenceMass)ersetzen