Epstein drag stopping time for spherical dust grains. More...

#include "shambase/assert.hpp"
#include "shambase/constants.hpp"
#include "shambackends/sycl.hpp"

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Functions
template<class T >
T	shamphys::epstein_supersonic_correction (T delta_v, T cs) noexcept
	Epstein drag supersonic correction factor.

template<class T >
T	shamphys::epstein_stopping_time (T rho_grain, T s_grain, T rho, T cs, T gamma, T f=T(1.0)) noexcept
	Epstein drag stopping time for spherical dust grains.

Detailed Description

Epstein drag stopping time for spherical dust grains.

Author: Timothée David–Cléris (tim.s.nosp@m.hamr.nosp@m.ock@p.nosp@m.roto.nosp@m.n.me)

Definition in file Dust.hpp.

Function Documentation

◆ epstein_stopping_time()

template<class T >

T shamphys::epstein_stopping_time	(	T	rho_grain,
		T	s_grain,
		T	rho,
		T	cs,
		T	gamma,
		T	f = `T(1.0)`
	)

inlinenoexcept

Epstein drag stopping time for spherical dust grains.

\[ t_s = \frac{\rho_{\rm grain} \, s_{\rm grain}}{\rho \, c_s \, f} \sqrt{\frac{\pi \gamma}{8}} \]

Corresponds to Eq. 250 in the PHANTOM paper.

where \(\rho = \rho_{\rm g} + \rho_{\rm d}\) is the total density, \(f\) is the supersonic correction (1.0 for the subsonic case), \(\gamma\) is the adiabatic index, \(\rho_{\rm grain}\) is the grain internal density, and \(s_{\rm grain}\) is the grain radius.

Parameters

rho_grain	Internal density of the dust grain
s_grain	Radius of the dust grain
rho	Total density ( \(\rho_{\rm g} + \rho_{\rm d}\))
cs	Gas sound speed
gamma	Adiabatic index
f	Supersonic correction factor (default 1.0)

Returns: Stopping time

Definition at line 75 of file Dust.hpp.

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◆ epstein_supersonic_correction()

template<class T >

T shamphys::epstein_supersonic_correction	(	T	delta_v,
		T	cs
	)

inlinenoexcept

Epstein drag supersonic correction factor.

Corrects the Epstein drag for supersonic drift between dust and gas. When the drift speed exceeds the gas thermal speed, the relative motion must be accounted for in the drag force.

\[ f(\Delta v, c_s) = \sqrt{1 + \frac{9\pi}{128} \frac{\Delta v^2}{c_s^2}} \]

Corresponds to Eq. 249 in the PHANTOM paper.