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Dust in AstroBEAR - Update 2019/10/14

(Can't make it to today's meeting due to a time conflict with a seminar I am required to attend. Back next week!)

Current Objective

Developing the dust drag advection routines (collisional drag)

Current Status

Collisional drag subroutine is implemented though simulations crash with the following error message: "Src Error::RKOrder45 — timestep insignificant. Halting." I'm currently checking whether this is a bug in the source routine I've set up resulting in an unrealistically rapid dust acceleration or whether the system is too stiff.

Supporting Material

Gas Drag Equations (for Collisional Drag)

The new dust velocity after one time-setp is given by:

\vec{v}_{\textrm{dust}}(t + \bigtriangleup t) = \vec{v}_{\textrm{dust}} (t) + \bigtriangleup \vec{v}_{\textrm{dust}}(t) \, ,

where

\bigtriangleup \vec{v}_{\textrm{dust}} (t) = \frac{\vec{F}_{\textrm{drag}} (t)}{m} \cdot \bigtriangleup t\, .

The drag force \vec{F}_{\textrm{drag}} is given by

\vec{F}_{\textrm{drag}} = 2 \sqrt{\pi} k_B T_{\textrm{gas}} a^2 \sum_j n_{\textrm{gas,j}} \mathcal{F}_{\textrm{col,j}}\,.

The sum over j covers all particles species in the gas (we are using an average value for an oxygen dominated SNR). \mathcal{F}_{\textrm{col,j}} is given by:

\mathcal{F}_{\textrm{col,j}} = \left( S_j + \frac{1}{2 \cdot S_j} \right) \cdot e^{-S_j^2} + \sqrt{\pi} \left(S_j^2 + 1 - \frac{1}{4 \cdot S_j^2} \right) \cdot erf{S_j} \, ,

where S_j is

S_j = \sqrt{\frac{m_{\textrm{gas,j}}}{2 \cdot k_B \cdot T_{\textrm{gas}}}} \cdot v_{\textrm{rel}} .

The remaining variables are (all in cgs):

m: mass of a dust grain
n_j: number density of gas species j
T_{\textrm{gas}}: gas temperatire
a: grain radius
m_{\textrm{gas,j}}: mass of a gas particle of species j
v_{\textrm{rel}}: absolute value of the relative velocity between gas and dust
\bigtriangleup t: timestep

The resulting drag force is then multiplied with a scaled unit vector to extract the drag forces in each dimension.

(Refernces: Kirchschlager et al. 2019, Baines et al. 1965, Draine & Salpeter 1979)

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