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source.cpp
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source.cpp
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/**
* source.cpp
*
* This file contains routines pertaining to the gravitation and friction sources.
*
*
*/
#define EIGEN_RUNTIME_NO_MALLOC
#include <cassert>
#include "aiolos.h"
///////////////////////////////////////////////////////////
//
// Gravitation
//
//
///////////////////////////////////////////////////////////
/**
* Initialize the gravity array with a non-self gravitating solution and the tidal field.
* Computes rhill which is output in the beginning of the run.
*/
void c_Sim::init_grav_pot() {
double rh = planet_semimajor * au * pow(planet_mass / (3.* star_mass ),0.333333333333333333);
for(int i = 1; i <= num_cells+1; i++) {
enclosed_mass[i] = planet_mass; //No self-gravity
phi[i] = get_phi_grav(x_i12[i], enclosed_mass[i]);
if(use_tides == 1) {
//if(x_i[i]>0.2*rh)
phi[i] -=0.5* 3.*G*init_star_mass*x_i12[i]*x_i12[i]/pow(planet_semimajor*au,3.);
}
//phi[i] -=0.5* 3.*G*star_mass*x_i12[i]*x_i12[i]/pow(planet_semimajor*au,3.);
}
phi[0] = get_phi_grav(x_i12[1], planet_mass);
rhill = planet_semimajor*au * std::pow(planet_mass / 3. / star_mass, 0.333333333333333333333);
}
/**
* Compute the integrated mass in shells and the gravity array as a self-gravitating solution
*/
void c_Sim::update_mass_and_pot() {
double species_dens_sum;
if(debug >= 1)
cout<<"In update mass. "<<endl;
enclosed_mass[0] = planet_mass;
enclosed_mass[1] = planet_mass; //Ghosts
for(int i = 2; i <= num_cells; i++) {
//Loop over all species densities
species_dens_sum = 0.;
for(int s = 0; s < num_species; s++)
species_dens_sum += species[s].u[i].u1;
double xn3 = x_i[i];
xn3 = xn3*xn3*xn3;
double xl3 = x_i[i-1];
xl3 = xl3*xl3*xl3;
enclosed_mass[i] = enclosed_mass[i-1] + 4. * 3.141592 * (xn3 - xl3)/3. * species_dens_sum; //Straightfoward integration of the poisson eqn
if (use_self_gravity == 1)
phi[i] = get_phi_grav(x_i12[i], enclosed_mass[i]);
else
phi[i] = get_phi_grav(x_i12[i], enclosed_mass[0]);
//if use tidal gravity
if(use_tides == 1) {
double d3 = planet_semimajor*au;
double rh = planet_semimajor * au * pow(planet_mass / (3.* star_mass ),0.333333333333333333);
double m0 = init_star_mass;
double m1 = star_mass;
double t0 = ramp_star_mass_t0;
double t1 = ramp_star_mass_t1;
double a = (m0-m1)/(t0-t1);
double b = 0.5*(m0+m1 - a *(t1+t0));
double current_star_mass = m0;
if(globalTime > t0)
current_star_mass = a * globalTime + b;
if(globalTime > t1)
current_star_mass = star_mass;
//if(steps==5)
// cout<<" In tidal grav, t0/t1 = "<<t0<<"/"<<t1<<" m0/current_mass ="<<m0/msolar<<"/"<<current_stellar_mass/msolar<<endl;
d3 = d3*d3*d3;
//if(x_i[i]>0.2*rh)
phi[i] -= 0.5* 3.*G*star_mass*x_i12[i]*x_i12[i]/d3;
}
}
if(debug >= 1)
cout<<"Done in update mass and pot. "<<endl;
}
//
/**
* Helper function implementing the actual gravity law used (i.e. $\phi \propto -1/r$ or $\phi \propto +z^2$). Works also in cartesian coordinates
* Options: linear gravity and 1/r gravity with gravitational smoothing from Klahr&Kley 2006
*
* @param[in] r physical, intercell radii in cm
* @param[in] mass physical mass inside shells of radii r in g
* @return grav potential in erg/g
*/
double c_Sim::get_phi_grav(double &r, double &mass) {
//
// Deepening the potential if needed
//
if(globalTime < rs_time) {
rs_at_moment = 0.5 - (0.5 + rs) * (globalTime/rs_time) ;
}
else
rs_at_moment = rs;
//
// Linear or 1/r gravity
//
if(use_linear_gravity)
return -G*mass*abs(domain_max - r);
else
{
if(abs(r-planet_position) > rs_at_moment )
return -G*mass/abs(r-planet_position);
else
return -G*mass * (pow(r-planet_position,3.)/pow(rs_at_moment,4.) - 2.* pow(r-planet_position,2.)/pow(rs_at_moment,3.) + 2./rs_at_moment );
}
}
/**
* Compute the well-balanced source function via the lhs and rhs grav potential differences for any cell-centered index j. After Eq. 11 in KäppeliMishra2016
* This function uses phi_s, the species-dependent gravitational potential. If the turbulent mixing parameter is 0, then phi_s = phi. If it is non-zero then phi_s regulates
* how different species feel a weaker field in the lower atmopshere, to adjust their scale height to the dominant species, assumed to be species[0].
*
* @param[in] u Conservative data in cell j
* @param[in] j Interface number
* @return The well-balanced potential difference in cell j
*/
AOS c_Species::source_grav(AOS &u, int &j) {
assert(j > 0 && j <= num_cells) ;
double dphidr_p = (phi_s[j] - phi_s[j-1]) / (base->dx[j] + base->dx[j-1]) ;
double dphidr_m = (phi_s[j+1] - phi_s[j]) / (base->dx[j+1] + base->dx[j]) ;
return AOS(0, u.u1, u.u2) * (-1.) * ( base->omegaplus[j] * dphidr_p + base->omegaminus[j] * dphidr_m);
}
/**
* For scenarios using a changed lower atmospheric gravity field to equalize all scale heights for all species.
* Switched on using
* NOTE: Future applications might require modifying the loop to find homopause.
*
* @param[in] argument Species number. In current use this is identical to this->this_species_index, but the option should be open to point to one dominant species.
*/
void c_Species::update_kzz_and_gravpot(int argument) {
int homopause_boundary_i = 0;
double mu = base->species[0].mass_amu;
double mi = this->mass_amu;
if(argument > 0 && mi > 1e-3) { //Do the kzz buildup for all other species except atomic hydrogen (assumed species[0]) and no electrons (mass = 5e-4).
for(int i=0; i<num_cells+2; i++) {
double n = base->species[0].prim[i].number_density;
double kzz = base->K_zz[i]; //This is a meta-parameter for k_zz/b
double par = std::pow(n, 1./1.);
K_zzf[i] = (1. + kzz*par*mu/mi) / (1. + kzz*par);
if(kzz*n < 1.)
K_zzf[i] = 1.;
else
K_zzf[i] = mu/mi;
double one = 0.99999;
if(K_zzf[i] > one && K_zzf[i-1] < one) //found homopause
homopause_boundary_i = i;
}
}
else {
for(int i=0; i<num_cells+2; i++) {
K_zzf[i] = 1.;
}
}
for(int i=0; i<num_cells+2; i++) {
phi_s[i] = base->phi[i] * K_zzf[i];
}
double phicorrection = base->phi[homopause_boundary_i]*(1.-mu/mi); //Correct for the jump in Phi at the homopause
if(homopause_boundary_i == 0)
phicorrection = 0;
for(int i=0; i<homopause_boundary_i; i++)
phi_s[i] += phicorrection;
//cout<<"s = "<<argument<<" phicorr = "<<phicorrection<<" homopause_i = "<<homopause_boundary_i<<endl;
//cout<<"Finished updating kzz in species "<<speciesname<<endl;
}
///////////////////////////////////////////////////////////
//
// Friction
//
//
///////////////////////////////////////////////////////////
/**
* Wrapper function calling the appropriate analytical or numerical functions.
*/
void c_Sim::compute_drag_update() {
//cout<<"In drag_update"<<endl;
if(friction_solver >= 0 && num_species > 1) {
if(friction_solver == 0)
compute_friction_analytical();
else{
//cout<<"calling friction numerical"<<endl;
compute_friction_numerical();
}
}
}
/**
* Friction solver 0. Only works for two species properly. Three species solution was copied&converted from mathematica matrix inversion, but produces nonsense.
*/
void c_Sim::compute_friction_analytical() {
if(debug > 0) cout<<"in analytic friction, num_species = "<<num_species<<endl;
if(num_species == 2) {
//Apply analytic solutions
double alpha=0, eps=0, f1=0, f2=0;
double v1b=0, v2b=0, v1a=0, v2a=0;
double coll_b;
double mumass, meanT, m0, m1;
for(int j=0; j <= num_cells+1; j++){
v1b = species[0].prim[j].speed;
v2b = species[1].prim[j].speed;
if(collision_model == 'C') {
alpha = alpha_collision;
} else {
// Physical model
m0 = species[0].mass_amu*amu;
m1 = species[1].mass_amu*amu;
mumass = m0 * m1 / (m0 + m1);
meanT = (m1 * species[0].prim[j].temperature + m0 * species[1].prim[j].temperature) / (m0 + m1);
if (species[0].is_dust_like || species[1].is_dust_like) {
// Use Epstein drag law (Hard sphere model)
double RHO_DUST = 1;
double s0=0, s1=0 ;
if (species[0].is_dust_like)
s0 = std::pow(3*m0/(4*M_PI*RHO_DUST), 1/3.) ;
if (species[0].is_dust_like)
s1 = std::pow(3*m1/(4*M_PI*RHO_DUST), 1/3.) ;
double A = M_PI*(s0+s1)*(s0+s1) ;
double v_th = std::sqrt(8*kb*meanT/(M_PI * mumass)) ;
alpha = 4/3. * species[1].prim[j].density * v_th * A/(m0+m1) ;
} else { // Gas-gas collisions
coll_b = 5.0e17 * std::pow(meanT, 0.75) ; // from Zahnle & Kasting 1986 Tab. 1
alpha = kb * meanT * species[1].prim[j].number_density / (m0 * coll_b) ; // From Burgers book, or Schunk & Nagy.
alpha *= alpha_collision;
}
}
alphas_sample(j) = alpha;
friction_sample(j) = alphas_sample(j) * (v2b - v1b);
eps = species[0].u[j].u1 / species[1].u[j].u1;
f1 = (1. + dt*alpha)/(1. + dt*alpha*(1.+eps)) ;
f2 = dt*alpha*eps / (1. + dt * alpha);
v2a = (v2b + v1b * f2 ) * f1;
v1a = v1b - (v2a - v2b) / eps;
species[0].prim[j].speed = v1a;
species[1].prim[j].speed = v2a;
if(debug >= 1) {
//cout<<" v1b, v2b = "<<v1b<<" "<<v2b<<endl<<" v1a, v2a = "<<v1a<<" "<<v2a<<endl;
//cout<<" dv1, dv2 = "<<v1a-v1b<<" "<<v2a-v2b<<endl;
//cout<<" dp1, dp2 = "<<(v1a-v1b)*species[0].u[j].u1 + (v2a-v2b)*species[1].u[j].u1<<endl;
cout<<" dt*alpha = "<<dt*alpha<<" alpha = "<<alpha<<" eps = "<<species[1].u[j].u1/species[0].u[j].u1<<" dmom/|mom| = "<<((v1a-v1b)*species[0].u[j].u1 + (v2a-v2b)*species[1].u[j].u1)/(std::sqrt(species[0].u[j].u2*species[0].u[j].u2) + std::sqrt(species[1].u[j].u2*species[1].u[j].u2) )<<" meanT = "<<meanT<<" coll_b = "<<coll_b<<" cell = "<<j<<endl;
}
double v_half = 0.5*(v1a + v1b) - 0.5*(v2a + v2b) ;
double v_end = v1a - v2a ;
species[0].prim[j].internal_energy += dt * alpha * (species[1].mass_amu/(species[0].mass_amu+species[1].mass_amu)) * v_half * v_end ;
species[1].prim[j].internal_energy += dt * alpha * eps * (species[0].mass_amu/(species[0].mass_amu+species[1].mass_amu)) * v_half * v_end ;
}
if(debug > 0) {
double dekin1 = 0.5*species[0].u[num_cells+1].u1 * (v1a - v1b) * (v1a - v1b) ;
double dekin2 = 0.5*species[1].u[num_cells+1].u1 * (v2a - v2b) * (v2a - v2b) ;
double dvrel1 = (v1a - v1b)/v1b;
double dvrel2 = (v2a - v2b)/v2b;
cout<<"Relative differences in velocities 1/2 = "<<dvrel1<<" / "<<dvrel2<<" differences in Ekin = "<<dekin1<<" / "<<dekin2<<endl;
char a;
cin>>a;
}
}
if(num_species == 3) { //Experimental 3-species solution
double det;
double v1a=0, v2a=0, v3a=0, v1b=0, v2b=0, v3b=0;
Eigen::Matrix3d a = Eigen::Matrix3d::Zero();
Eigen::Vector3d dens_vector(0,0,0);
if(debug > 0) cout<<" Before radial loop. a ="<<a<<endl;
for(int j=0; j <= num_cells+1; j++){
if(debug > 1) cout<<" Before species loop."<<endl;
for(int si=0; si<num_species; si++) {
dens_vector(si) = species[si].u[j].u1;
}
v1b = species[0].prim[j].speed;
v2b = species[1].prim[j].speed;
v3b = species[2].prim[j].speed;
if(debug > 1) cout<<" Before coeff loop."<<endl;
for(int si=0; si<num_species; si++)
for(int sj=0; sj<num_species; sj++)
{
if(si==sj)
a(si,sj) = 0.;
else if(si > sj)
a(si,sj) = friction_coeff_mask(si,sj) * alpha_collision;
else
a(si,sj) = friction_coeff_mask(si,sj) * alpha_collision * dens_vector(sj) / dens_vector(si);
}
if(debug > 1) cout<<" Before radial loop."<<endl;
det = - ( a(0, 2) + dt* a(0, 2) * a(1, 0) + a(0, 1) * a(1, 2) +dt* a(0, 2)* a(1, 2)) * a(2, 0);
det += (-a(0, 2) * a(1, 0) - a(1, 2) -dt* a(0, 1)* a(1, 2) - dt* a(0, 2)* a(1, 2)) * a(2, 1);
det += (-a(0, 1) * a(1, 0) + (1. + dt* (a(0, 1) + a(0, 2) ))* (1. +dt* (a(1, 0) + a(1, 2)))) *(1. +dt *(a(2, 0) + a(2, 1)));
v1a = v1b*(-a(1, 2) * a(2, 1) + (1. + dt* (a(1, 0) + a(1, 2))) * (1. + dt * (a(2, 0) + a(2, 1))));
v1a += v2b*( a(0, 1) + dt * a(0, 1) * a(2, 0) + dt * a(0, 1) * a(2, 1) + a(0, 2)* a(2, 1));
v1a += v3b*(a(0, 2) + dt * a(0, 2)* a(1, 0) + a(0, 1) * a(1, 2) + dt * a(0, 2)* a(1, 2));
v2a = v1b*(a(1, 0) + dt * a(1, 0) * a(2, 0) + a(1, 2)* a(2, 0) + dt * a(1, 0) * a(2, 1));
v2a += v2b*( -a(0, 2) * a(2, 0) + (1. + dt * (a(0, 1)* + a(0, 2))) * (1. + dt * (a(2, 0) + a(2, 1) ) )) ;
v2a += v3b*( a(0, 2) * a(1, 0) + a(1, 2) + dt * a(0, 1) * a(1, 2) + dt * a(0, 2) * a(1, 2));
v3a = v1b*(a(2, 0) + dt * a(1, 0) * a(2, 0) + dt * a(1, 2) * a(2, 0) + a(1, 0) * a(2, 1) );
v3a += v2b*(a(0, 1)* a(2, 0) + a(2, 1) + dt * a(0, 1) * a(2, 1) + dt * a(0, 2) * a(2, 1) );
v3a += v3b*(-a(0, 1)* a(1, 0) + (1. + dt* (a(0, 1) + a(0, 2)) ) * (1. + dt * (a(1, 0) + a(1, 2)) ) );
v1a /= det;
v2a /= det;
v3a /= det;
species[0].prim[j].speed = v1a;
species[1].prim[j].speed = v2a;
species[2].prim[j].speed = v3a;
species[0].prim[j].internal_energy += dt * a(0,1) * (species[1].mass_amu/(species[0].mass_amu+species[1].mass_amu))
* pow( v1a - v2a, 2.);
species[0].prim[j].internal_energy += dt * a(0,2) * (species[2].mass_amu/(species[0].mass_amu+species[2].mass_amu))
* pow( v1a - v3a, 2.);
species[1].prim[j].internal_energy += dt * a(1,0) * (species[0].mass_amu/(species[1].mass_amu+species[0].mass_amu))
* pow( v1a - v2a, 2.);
species[1].prim[j].internal_energy += dt * a(1,2) * (species[2].mass_amu/(species[1].mass_amu+species[2].mass_amu))
* pow( v2a - v3a, 2.);
species[2].prim[j].internal_energy += dt * a(2,0) * (species[0].mass_amu/(species[2].mass_amu+species[0].mass_amu))
* pow( v1a - v3a, 2.);
species[2].prim[j].internal_energy += dt * a(2,1) * (species[1].mass_amu/(species[2].mass_amu+species[1].mass_amu))
* pow( v2a - v3a, 2.);
///TODO: Internal energy update, if 3-species solver ever works.
}
if(debug > 0) {
char b;
double dekin1 = 0.5*species[0].u[num_cells+1].u1 * (v1a - v1b) * (v1a - v1b) ;
double dekin2 = 0.5*species[1].u[num_cells+1].u1 * (v2a - v2b) * (v2a - v2b) ;
double dvrel1 = (v1a - v1b)/v1b;
double dvrel2 = (v2a - v2b)/v2b;
cout<<"alpha_collision ="<<alpha_collision<<" det = "<<det<<" a(0,0)="<<a(0,0)<<" matrix a = "<<a<<endl;
cout<<"Relative differences in velocities 1/2 = "<<dvrel1<<" / "<<dvrel2<<" differences in Ekin = "<<dekin1<<" / "<<dekin2<<endl;
cin>>b;
}
}
if(debug > 0) {
cout<<"in friction, pos2 num_cells = "<<num_cells<<endl;
char a;
cin>>a;
}
for(int s=0; s<num_species; s++){
species[s].eos->update_p_from_eint(&(species[s].prim[0]), num_cells+2);
species[s].eos->compute_conserved(&(species[s].prim[0]), &(species[s].u[0]), num_cells+2);
}
}
/**
* Friction solver 1: Compute collision coefficients, build collision matrix and solve in a fast way
* Collision coefficients are hard-coded in compute_alpha_matrix().
*/
void c_Sim::compute_friction_numerical() {
Eigen::internal::set_is_malloc_allowed(false) ;
if(debug > 0) cout<<"in numerical, dense friction, num_species = "<<num_species<<endl;
for(int j=0; j <= num_cells+1; j++){
fill_alpha_basis_arrays(j);
compute_alpha_matrix(j);
if(debug >= 2 && j==1200 && steps == 10) {
cout<<" Computed coefficient matrix ="<<endl<<friction_coefficients<<endl;
cout<<" velocities ="<<endl<<friction_vec_input<<endl;
cout<<" velocities[0] = "<<friction_vec_input(0)<<endl;
cout<<" rho[0] = "<<species[0].u[j].u1<<endl;
}
friction_matrix_T = identity_matrix - friction_coefficients * dt;
friction_matrix_T.diagonal().noalias() += dt * (friction_coefficients * unity_vector);
LU.compute(friction_matrix_T) ;
friction_vec_output.noalias() = LU.solve(friction_vec_input);
if(debug >= 3 && j==700 && steps == 10) {
cout<<" T = "<<endl<<friction_matrix_T<<endl;
cout<<" a10/a01 = "<<friction_matrix_T(0,1)/friction_matrix_T(1,0)<<" dens(0)/dens(1) = "<<dens_vector(1)/dens_vector(0)<<" dt*a*eps = "<<friction_coefficients(0,1) * dt * dens_vector(0)/dens_vector(1)<<endl;
cout<<" v_inp = "<<endl<<friction_vec_input<<endl;
cout<<" v_out = "<<endl<<friction_vec_output<<endl;
cout<<" dv_ = "<<endl<<friction_vec_output-friction_vec_input<<endl;
cout<<" dp = "<<(friction_vec_output(0)-friction_vec_input(0))*dens_vector(0)<<" + "<<(friction_vec_output(1)-friction_vec_input(1))*dens_vector(1)<<" = "<<(friction_vec_output(0)-friction_vec_input(0))*dens_vector(0) + (friction_vec_output(1)-friction_vec_input(1))*dens_vector(1)<<endl;
cout<<" friction_coeff ="<<endl<<friction_matrix_T<<endl;
cout<<" friction_coeff ="<<endl<<friction_matrix_T(0,1)/dt<<endl;
cout<<" dt * alpha01 = "<<endl<<friction_matrix_T(0,1)<<endl;
cout<<" dt * alpha01 * eps = "<<endl<<friction_matrix_T(0,1) * dens_vector(0)/dens_vector(1)<<endl;
char a;
cin>>a;
}
//*/
// Update new speed and internal energy
//
for(int si=0; si<num_species; si++)
species[si].prim[j].speed = friction_vec_output(si);
for(int si=0; si<num_species; si++) {
double temp = 0;
for(int sj=0; sj<num_species; sj++) {
double v_end = friction_vec_output(si) - friction_vec_output(sj) ;
double v_half = 0.5*(v_end + friction_vec_input(si) - friction_vec_input(sj)) ;
temp += dt * friction_coefficients(si,sj) * (species[sj].mass_amu/(species[sj].mass_amu+species[si].mass_amu)) * v_half * v_end ;
if(si==0 && sj == 1) {
friction_sample(j) = alphas_sample(j) * (friction_vec_input(si) - friction_vec_input(sj));
}
}
species[si].prim[j].internal_energy += temp;
}
}
//
// Update conserved
//
for(int si=0; si<num_species; si++) {
species[si].eos->update_p_from_eint(&(species[si].prim[0]), num_cells+2);
species[si].eos->compute_conserved(&(species[si].prim[0]), &(species[si].u[0]), num_cells+2);
}
}
/**
* Build all primitives that we need multiple times during the construciton of the alpha matrix
*
* @param[in] j Cell number in which to compute the temp data
*/
void c_Sim::fill_alpha_basis_arrays(int j) { //Called in compute_friction() in source.cpp
for(int si=0; si<num_species; si++) {
friction_vec_input(si) = species[si].prim[j].speed;
dens_vector(si) = species[si].u[j].u1;
numdens_vector(si) = species[si].prim[j].number_density;
mass_vector(si) = species[si].mass_amu*amu;
temperature_vector(si) = species[si].prim[j].temperature;
temperature_vector_augment(si) = species[si].prim[j].temperature - dt * (species[si].dS(j) + species[si].dG(j)) / species[si].u[j].u1 / species[si].cv;
}
}
/**
* Build collision matrix. Here we also distinguish between gas/dust species and between charged/neutral species in terms of collission coefficients.
*
* * @param[in] j Cell number in which to build the collision matrix
*/
void c_Sim::compute_alpha_matrix(int j) { //Called in compute_friction() and compute_radiation() in source.cpp
if(steps< 4 && j ==100)
cout<<steps<<" In compute_alpha_matrix j==100"<<endl;
double alpha_local;
double coll_b;
//double mtot;
double mumass, mumass_amu, meanT;
for(int si=0; si<num_species; si++) {
for(int sj=0; sj<num_species; sj++) {
if(collision_model == 'C') { //Constant drag law
alpha_local = alpha_collision;
if (si > sj) alpha_local *= dens_vector(sj) / dens_vector(si) ;
} else {
if(si==sj) {
alpha_local = 0.;
} else { // Physical drag laws
//mtot = mass_vector(si) + mass_vector(sj);
mumass = mass_vector(si) * mass_vector(sj) * inv_totmasses(si,sj); /// (mass_vector(si) + mass_vector(sj));
mumass_amu = mumass/amu;
meanT = (mass_vector(sj)*temperature_vector(si) + mass_vector(si)*temperature_vector(sj)) * inv_totmasses(si,sj); // / (mass_vector(si) + mass_vector(sj)); //Mean collisional mu and T from Schunk 1980
if (species[si].is_dust_like || species[sj].is_dust_like) { //One of the collision partners is dust
// Use Epstein drag law (Hard sphere model)
double RHO_DUST = 1;
double s0=0, s1=0 ;
if (species[si].is_dust_like)
s0 = std::pow(3*mass_vector(si)/(4*M_PI*RHO_DUST), 1/3.) ;
if (species[sj].is_dust_like)
s1 = std::pow(3*mass_vector(sj)/(4*M_PI*RHO_DUST), 1/3.) ;
double A = M_PI*(s0+s1)*(s0+s1) ;
double v_th = std::sqrt(8*kb*meanT/(M_PI * mumass)) ;
alpha_local = 4/3. * dens_vector(sj) * v_th * A * inv_totmasses(si,sj) ;
} else { // Gas-gas collisions. Used binary diffusion coefficient
int ci = (int)(species[si].static_charge*1.01);
int cj = (int)(species[sj].static_charge*1.01);
double qn = (std::fabs(species[si].static_charge) + std::fabs(species[sj].static_charge));
//string ccase = ""; //Debug string to make sure the cases are picked right
if(std::abs(ci) + std::abs(cj) == 0) { //n-n collision
coll_b = 5.0e17 * std::sqrt(std::sqrt(meanT*meanT*meanT)) ; //std::pow(meanT, 0.75) // from Zahnle & Kasting 1986 Tab. 1
alpha_local = kb * meanT * numdens_vector(sj) * species[si].inv_mass / coll_b ; // From Burgers book, or Schunk & Nagy.
//ccase = " n-n ";
}
else if(std::abs(ci) == 0 || std::abs(cj) == 0) {//i-n collision
if(species[si].mass_amu < 1.1 && species[sj].mass_amu < 1.1) { //Resonant H,H+ collisions
alpha_local = 2.65e-10 * numdens_vector(sj) * std::sqrt(meanT) * std::pow((1. - 0.083 * std::log10(meanT)), 2.);
//ccase = "resonant H-p+ ";
} else {
alpha_local = 1*2.21 * 3.141592 * numdens_vector(sj) * mass_vector(sj) * inv_totmasses(si,sj); // /(mass_vector(sj)+mass_vector(si));
alpha_local *= std::sqrt(0.66 / mumass ) * 1e-12 * qn * elm_charge; //0.66 is the polarizability of neutral atomic H
alpha_local *= resonant_pair_matrix(si,sj); //Crude way to emulate resonant collision cross-sections: pairs are multiplied by 10, everything else by 1
//ccase = "resonant or nonresonant i-n ";
}
}
else { //i-i collision
alpha_local = alpha_collision_ions * 1.27 * species[si].static_charge * species[si].static_charge * species[sj].static_charge * species[sj].static_charge * std::sqrt(mumass_amu) * amu * species[si].inv_mass; // / mass_vector(si);
alpha_local *= numdens_vector(sj) / std::sqrt(meanT*meanT*meanT);
//ccase = " i-i ";
}
if(si!=sj && debug>3)
cout<<"cell "<<j<<" colliding "<<species[si].speciesname<<" q="<<species[si].static_charge<<" with "<<species[sj].speciesname<<" q="<<species[sj].static_charge<<" ccase = "<<" alpha/n = "<<alpha_local/ numdens_vector(sj)<<" n_sj = "<<numdens_vector(sj)<<endl;
double alpha_temp = alpha_collision;
if(globalTime < coll_rampup_time) { //Ramp up the friction factors linearly, if so desired
alpha_temp = alpha_collision * ( init_coll_factor + (1.-init_coll_factor) * globalTime/coll_rampup_time );
} else {
alpha_temp = alpha_collision;
}
//alpha_local *= alpha_collision;
alpha_local *= alpha_temp;
}
}
}
if(si==0 && sj == 1) {
alphas_sample(j) = alpha_local; //alphas_sample is saving alpha values for later use outside of the friction function, e.g. to output it
//cout<<" spec "<<species[si].name<<" j = "<<j<<" alpha_local = "<<alpha_local<<endl;
if(debug > 0 && steps == 1 && ((j==2) || (j==num_cells-2) || (j==num_cells/2)) )
cout<<" spec "<<species[si].speciesname<<" j = "<<j<<" alpha_local = "<<alpha_local<<endl;
}
// Fill alpha_ij and alpha_ji
//if(si==sj)
// friction_coefficients(si,sj) = 0.;
//else
friction_coefficients(si,sj) = friction_coeff_mask(si,sj) * alpha_local;
//friction_coefficients(sj,si) = friction_coeff_mask(sj,si) * alpha_local * dens_vector(si) / dens_vector(sj);
//alpha_local *= ;
}
}
//char a;
//cin>>a;
}
/**
* Build collisional heat exchange matrix. Uses pre-computed values from momentum transfer.
* Called from compute_collisional_heat_exchange.
* 21 May 2023: This function has been disabled in radiation_simple, the coefficients are computed in place there now
*
* * @param[in] j Cell number in which to build the heat exchange matrix
*/
void c_Sim::compute_collisional_heat_exchange_matrix(int j) {
// Get the alpha matrix
compute_alpha_matrix(j) ;
// Convert to collision matrix
for(int si=0; si<num_species; si++) {
double diag_sum = 0 ;
for(int sj=0; sj<num_species; sj++) {
friction_coefficients(si, sj) *=
3 * kb / (species[si].cv * (mass_vector(si) + mass_vector(sj))) ;
diag_sum += friction_coefficients(si, sj) ;
}
// Set the diagonal to sum of Ti terms.
friction_coefficients(si, si) -= diag_sum ;
}
}
/**
* Solve for collisional heat exchange
*/
void c_Sim::compute_collisional_heat_exchange() {
Eigen::internal::set_is_malloc_allowed(false) ;
if (num_species == 1)
return ;
if(debug > 0)
cout << "in compute_collisional_heat_exchange, num_species = "
<< num_species << endl;
for(int j=0; j <= num_cells+0; j++){
fill_alpha_basis_arrays(j);
compute_collisional_heat_exchange_matrix(j);
// Solve implicit equation for new temperature
friction_matrix_T = identity_matrix - friction_coefficients * dt;
LU.compute(friction_matrix_T) ;
friction_vec_input.noalias() = LU.solve(temperature_vector_augment);
// Set friction_vec_output to dT/dt:
friction_vec_output =
friction_coefficients * friction_vec_input ;
//
// Update internal energy (dE = Cv dT/dt * dt)
//
for(int si=0; si<num_species; si++) {
species[si].prim[j].internal_energy += species[si].cv*friction_vec_output(si)*dt;
species[si].prim[j].temperature += friction_vec_output(si)*dt;
}
}
//
// Update conserved quantities
//
for(int si=0; si<num_species; si++) {
species[si].eos->update_p_from_eint(&(species[si].prim[0]), num_cells+2);
species[si].eos->compute_conserved(&(species[si].prim[0]), &(species[si].u[0]), num_cells+2);
}
}