/* ********************************************************************* */
void Init (double *v, double x1, double x2, double x3)
/*!
* The Init() function can be used to assign initial conditions as
* as a function of spatial position.
*
* \param [out] v a pointer to a vector of primitive variables
* \param [in] x1 coordinate point in the 1st dimension
* \param [in] x2 coordinate point in the 2nd dimension
* \param [in] x3 coordinate point in the 3rd dimension
*
* The meaning of x1, x2 and x3 depends on the geometry:
* \f[ \begin{array}{cccl}
* x_1 & x_2 & x_3 & \mathrm{Geometry} \\ \noalign{\medskip}
* \hline
* x & y & z & \mathrm{Cartesian} \\ \noalign{\medskip}
* R & z & - & \mathrm{cylindrical} \\ \noalign{\medskip}
* R & \phi & z & \mathrm{polar} \\ \noalign{\medskip}
* r & \theta & \phi & \mathrm{spherical}
* \end{array}
* \f]
*
* Variable names are accessed by means of an index v[nv], where
* nv = RHO is density, nv = PRS is pressure, nv = (VX1, VX2, VX3) are
* the three components of velocity, and so forth.
*
*********************************************************************** */
{
/* Density normalization */
real mu = MeanMolecularWeight(v);
g_unitDensity = CONST_amu*mu;
/* Upstream Mach number and temperature
This determines velocity normalization
which is the value of the upstream velocity */
double mach = g_inputParam[PAR_MACH];
double temp1_cgs = g_inputParam[PAR_TEMP];
double csound_cgs = sqrt(g_gamma*CONST_kB*temp1_cgs/(CONST_amu*mu));
g_unitVelocity = csound_cgs*mach;
/* Upstream vector */
double v1[NVAR];
v1[RHO] = g_inputParam[PAR_RHO1];
EXPAND(v1[VX1] = 1.0;,
/* ***************************************************************** */
void PowerLawCooling (Data_Arr VV, real dt, Time_Step *Dts, Grid *grid)
/*
*
* PURPOSE:
*
* Take a source step to account for radiative cooling with
* a power-law cooling function.
*
* We directly integrate the following ODE:
*
* dp_cgs/dt_cgs = -(gamma - 1) Lambda(rho_cgs, T_cgs)
*
* where: Lambda = lambda0 rho_cgs^2/(mu*m_amu,cgs)^2 (T_cgs/T_crit,cgs)^alpha
*
* if the cooling function was a single power law.
*
*
*
******************************************************************* */
{
int i, j, k;
real cost, dE;
real rho, p, T, p_f, T_f;
real oma, unit_time;
/* Read cooling parameters file */
/* Power law cooling mainly valid in regions 10^5
The values for alpha and lamdbda0 just come from a linear fit to the
cooltable.dat data between T = 3*10^4 and 1*10^8 K. See cool_fit_pow.py
*/
double alpha = -0.37988772;
double lambda0 = 1.044886865e-22;
/* Mean molecular mass */
double vdummy[NVAR];
real mu = MeanMolecularWeight(vdummy);
/* A constant that is part of the solution. */
cost = (g_gamma-1.0)*lambda0/CONST_kB*pow(g_minCoolingTemp, -alpha);
/* Unit time code to cgs conversion */
unit_time = g_unitLength/g_unitVelocity;
/* -------------------------------------------------------------
Integrate analytically
------------------------------------------------------------- */
//dE = 1.e-18;
DOM_LOOP(k,j,i){
/* ---- Find initial temperature in Kelvin ---- */
rho = VV[RHO][k][j][i];
p = VV[PRS][k][j][i];
T = mu*p/rho*KELVIN;
if (T < g_minCoolingTemp) continue;
/* ---- Find final temperature ---- */
/* rho is in code units because the factor in the equation reads
* (rho/mu amu), but all other quantities are in cgs */
oma = 1.-alpha;
T_f = pow(-cost*oma*rho*dt*unit_time + pow(T, oma), 1./oma);
if (T_f <= g_minCoolingTemp){
T_f = T - g_maxCoolingRate*(T - g_minCoolingTemp);
}
else{
T_f = T - g_maxCoolingRate*(T - T_f);
}
//T_f = MAX(T_f, g_minCoolingTemp);
/* ---- Update Energy ---- */
p_f = T_f*rho/(mu*KELVIN);
VV[PRS][k][j][i] = p_f;
//dE = fabs(1.0 - p_f/p) + 1.e-18;
//Dts->dt_cool = MIN(Dts->dt_cool, dt*g_maxCoolingRate/dE);
}
}}
}
Radiat (v, rhs);
L = CoolCoeffs.Lrate; La = CoolCoeffs.La; Lb = CoolCoeffs.Lb; Lc = CoolCoeffs.Lc;
C = CoolCoeffs.Crate; Ca = CoolCoeffs.Ca; Cb = CoolCoeffs.Cb; Cc = CoolCoeffs.Cc;
R = CoolCoeffs.Rrate; Ra = CoolCoeffs.Ra; Rb = CoolCoeffs.Rb; Rc = CoolCoeffs.Rc;
de = CoolCoeffs.de;
X = v + NFLX;
dnel_dX = CoolCoeffs.dnel_dX;
N = v[RHO]*find_N_rho(); /* -- Total number density -- */
mu = MeanMolecularWeight(v);
T = v[PRS]/v[RHO]*KELVIN*mu;
/* -- compute the vector grad_X (mu) -- */
scrh = 1.0/CoolCoeffs.muD;
for (k = 0; k < n - 1; k++){
dmu_dX[k] = (CoolCoeffs.dmuN_dX[k]
- CoolCoeffs.dmuD_dX[k]*mu)*scrh;
}
/* -------------------------------------------------
Compute dX'/dX, dp'/dX with
k = 0....n - 2
l = 0....n - 2
/* ********************************************************************* */
void Radiat (double *v, double *rhs)
/*!
* Cooling for neutral or singly ionized gas: good up to about 35,000 K
* in equilibrium or shocks in neutral gas up to about 80 km/s.
* Assumed abundances in ab
* Uses t : Kelvin
* dene : electron density cm*-3
* fneut : hydrogen neutral fraction (adimensionale)
* ci,cr : H ionization and recombination rate coefficients
*
*
* em(1) = TOTAL EMISSIVITY : (ergs cm**3 s**-1)
* em(2) = Ly alpha + two photon continuum: Aggarwal MNRAS 202,
* 10**4.3 K
* em(3) = H alpha: Aggarwal, Case B
* em(4) = He I 584 + two photon + 623 (all n=2 excitations): Berrington
* &Kingston,JPB 20
* em(5) = C I 9850 + 9823: Mendoza, IAU 103, 5000 K
* em(6) = C II, 156 micron: Mendoza, 10,000 K
* em(7) = C II] 2325 A: Mendoza, 15,000 K
* em(8) = N I 5200 A: Mendoza, 7500 K
* em(9) = N II 6584 + 6548 A: Mendoza
* em(10) = O I 63 micron: Mendoza,2500 K
* em(11) = O I 6300 A + 6363 A: Mendoza, 7500 K
* em(12) = O II 3727: Mendoza
* em(13) = Mg II 2800: Mendoza
* em(14) = Si II 35 micron: Dufton&Kingston, MNRAS 248
* em(15) = S II 6717+6727: Mendoza
* em(16) = Fe II 25 micron: Nussbaumer&Storey
* em(17) = Fe II 1.6 micron
* em(18) = thermal energy lost by ionization
* em(19) = thermal energy lost by recombination (2/3 kT per
* recombination.
* The ionization energy lost is not included here.
*
*********************************************************************** */
{
int ii, k, status;
double T, mu, st, rho, prs, fn;
double N_H, n_el, cr, ci, rlosst, em[20], src_pr;
static double t00[18] = {0.0 , 0.0 , 1.18e5, 1.40e5, 2.46e5, 1.46e4,
92.1 , 6.18e4, 2.76e4, 2.19e4, 228.0 , 2.28e4,
3.86e4, 5.13e4, 410.0 , 2.13e4, 575.0 , 8980.0};
static double ep[18] = {0.0 , 0.0 , 10.2 , 1.89, 21.2 , 1.26,
0.0079, 5.33, 2.38 , 1.89, 0.0197, 1.96,
3.33 , 4.43, 0.0354, 1.85, 0.0495, 0.775};
static double critn[18] = {0.0 , 0.0 , 1.e10, 1.e10, 1.e10, 312.0,
0.849, 1.93e7, 124.0, 865.0, 1090.0, 3950.0,
177.0, 1.e10 , 16.8, 96.0, 580.0, 1130.0};
static double om[18] = {0.0 , 0.0 , 0.90, 0.35, 0.15 , 0.067,
0.63, 0.52, 0.90, 0.30, 0.0055, 0.19,
0.33, 8.0 , 2.85, 1.75, 0.3 ,0.39};
static double ab[18] = {0.0 , 0.0 , 1.0 , 1.0 , 0.1 , 0.0003,
0.0003, 0.0003 , 0.0001 , 0.0001 , 0.0006 , 0.0006,
0.0006, 0.00002, 0.00004, 0.00004, 0.00004, 0.00004};
static double fn1[20] = {0.0, 0.0, 0.0, 0.0, 0.0,
0.1, 1.0, 1.0, 0.0, 1.0,
0.0, 0.0, 1.0, 1.0, 1.0,
1.0, 1.0, 1.0, 0.0, 1.0};
static double fn2[20] = {0.0, 0.0, 1.0, 1.0, 1.0,
0.0, 0.0, 0.0, 1.0,-1.0,
1.0, 1.0,-1.0, 0.0, 0.0,
0.0, 0.0, 0.0, 1.0,-1.0};
static int first_call = 1;
static double E_cost, Unit_Time, N_H_rho;
if (first_call) {
E_cost = UNIT_LENGTH/UNIT_DENSITY/pow(UNIT_VELOCITY, 3.0);
Unit_Time = UNIT_LENGTH/UNIT_VELOCITY;
/* ------------------------------------------------------
conversion factor from total density to hydrogen
number density, i.e. nH = N_H_rho * rho
------------------------------------------------------ */
N_H_rho = UNIT_DENSITY/CONST_amu/(CONST_AH + frac_He*CONST_AHe + frac_Z*CONST_AZ);
first_call = 0;
}
/* -----------------------------------
Force fneut to stay between [0,1]
----------------------------------- */
v[X_HI] = MAX(v[X_HI], 0.0);
v[X_HI] = MIN(v[X_HI], 1.0);
/* ---------------------------------------------------
Compute temperature from rho, rhoe and fractions
--------------------------------------------------- */
rho = v[RHO];
mu = MeanMolecularWeight(v);
#if EOS == IDEAL
if (v[RHOE] < 0.0) v[RHOE] = g_smallPressure/(g_gamma-1.0);
prs = v[RHOE]*(g_gamma-1.0);
T = prs/rho*KELVIN*mu;
#else
status = GetEV_Temperature(v[RHOE], v, &T);
if (status != 0) {
T = T_CUT_RHOE;
v[RHOE] = InternalEnergy(v, T);
}
#endif
fn = v[X_HI];
/* --------------------------------------------------------
Set source terms equal to zero when the temperature
falls below g_minCoolingTemp
-------------------------------------------------------- */
/* if (T < g_minCoolingTemp){
a = b = src_pr = 0.0;
continue;
}
*/
if (mu < 0.0){
printf ("Negative mu in radiat \n");
exit(1);
}
st = sqrt(T);
N_H = N_H_rho*rho; /* -- number density of hydrogen N_H = N(HI) + N(HII) -- */
/* ---- coeff di ionizz. e ricomb. della particella fluida i,j ---- */
cr = 2.6e-11/st;
ci = 1.08e-8*st*exp(-157890.0/T)/(13.6*13.6);
n_el = N_H*(1.0 - fn + frac_Z); /* -- electron number density, in cm^{-3} -- */
rhs[X_HI] = Unit_Time*n_el*(-(ci + cr)*fn + cr);
em[1] = 0.0;
for (k = 2; k <= 17; k++){
em[k] = 1.6e-12*8.63e-6*om[k]*ep[k]*exp(-t00[k]/T)/st;
em[k] = em[k]*critn[k]*st/(n_el + critn[k]*st);
em[k] = em[k]*ab[k]*(fn1[k] + fn*fn2[k]);
em[1] = em[1] + em[k];
}
em[18] = ci*13.6*1.6e-12*fn;
em[19] = cr*0.67*1.6e-12*(1.0 - fn)*T/11590.0;
em[1] = em[1] + em[18] + em[19];
/* ---------------------------------------------------
rlosst is the energy loss in units of erg/cm^3/s;
it must be multiplied by cost_E in order to match
non-dimensional units.
Source term for the neutral fraction scales with
UNIT_TIME
--------------------------------------------------- */
rlosst = em[1]*n_el*N_H;
/*
rhs[PRS] = -E_cost*rlosst*(g_gamma - 1.0);
rhs[PRS] *= 1.0/(1.0 + exp( -(T - g_minCoolingTemp)/100.0));
*/
rhs[RHOE] = -E_cost*rlosst;
rhs[RHOE] *= 1.0/(1.0 + exp( -(T - g_minCoolingTemp)/100.0)); /* -- cutoff -- */
}
