smash::ThermLatticeNode Class Reference

#include <grandcan_thermalizer.h>

The ThermLatticeNode class is intended to compute thermodynamical quantities in a cell given a set of particles.

It accumulates the upper row of the energy-momentum tensor \( T^{\mu 0}\), net baryon density nb and net strangeness densities in the computational frame. From these quantities it allows to compute the local rest frame quantites: temperature T, chemical potentials mub and mus, the velocity of the local rest frame with respect to the computational frame.

An example of the intended use is:

ThermLatticeNode node; for (const ParticleData &particle: some_particles_list) { const double some_smearing_factor = ...; node.add_particle(particle, some_smearing_factor); } HadronGasEos eos = HadronGasEos(false); node.compute_rest_frame_quantities(eos);

Note that before calling the compute_rest_frame_quantities T, mu, p and e are set to zero.

Definition at line 48 of file grandcan_thermalizer.h.

Collaboration diagram for smash::ThermLatticeNode:

Public Member Functions
	ThermLatticeNode ()
	Default constructor of thermal quantities on the lattice returning thermodynamic quantities in computational frame. More...
void	add_particle (const ParticleData &p, double factor)
	Add particle contribution to Tmu0, nb and ns May look like unused at first glance, but it is actually used by update_lattice, where the node type of the lattice is templated. More...
void	add_particle_for_derivatives (const ParticleData &, double, ThreeVector)
	dummy function for update_lattice More...
void	compute_rest_frame_quantities (HadronGasEos &eos)
	Temperature, chemical potentials and rest frame velocity are calculated given the hadron gas equation of state object. More...
void	set_rest_frame_quantities (double T0, double mub0, double mus0, const ThreeVector v0)
	Set all the rest frame quantities to some values, this is useful for testing. More...
FourVector	Tmu0 () const
	Get Four-momentum flow of the cell. More...
double	nb () const
	Get net baryon density of the cell in the computational frame. More...
double	ns () const
	Get net strangeness density of the cell in the computational frame. More...
double	e () const
	Get energy density in the rest frame. More...
double	p () const
	Get pressure in the rest frame. More...
ThreeVector	v () const
	Get 3-velocity of the rest frame. More...
double	T () const
	Get the temperature. More...
double	mub () const
	Get the net baryon chemical potential. More...
double	mus () const
	Get the net strangeness chemical potential. More...

Private Attributes
FourVector	Tmu0_
	Four-momentum flow of the cell. More...
double	nb_
	Net baryon density of the cell in the computational frame. More...
double	ns_
	Net strangeness density of the cell in the computational frame. More...
double	e_
	Energy density in the rest frame. More...
double	p_
	Pressure in the rest frame. More...
ThreeVector	v_
	Velocity of the rest frame. More...
double	T_
	Temperature. More...
double	mub_
	Net baryon chemical potential. More...
double	mus_
	Net strangeness chemical potential. More...

Constructor & Destructor Documentation

smash::ThermLatticeNode::ThermLatticeNode

(

)

Default constructor of thermal quantities on the lattice returning thermodynamic quantities in computational frame.

Returns

Tmu0_ Four vector \(T^{\mu 0}\), nb_ Net baryon density at this location, ns_ Net strangeness density, e_ Energy density, v_ 3 vector velocity of local rest frame, T_ Temperature mub_ Net baryon chemical potential, mus_ Net strangeness chemical potential

Definition at line 23 of file grandcan_thermalizer.cc.

    : Tmu0_(FourVector()),
      nb_(0.0),
      ns_(0.0),
      e_(0.0),
      p_(0.0),
      v_(ThreeVector()),
      T_(0.0),
      mub_(0.0),
      mus_(0.0) {}

Member Function Documentation

void smash::ThermLatticeNode::add_particle	(	const ParticleData &	p,
		double	factor
	)

Add particle contribution to Tmu0, nb and ns May look like unused at first glance, but it is actually used by update_lattice, where the node type of the lattice is templated.

Definition at line 34 of file grandcan_thermalizer.cc.

                                                                           {
  Tmu0_ += part.momentum() * factor;
  nb_ += static_cast<double>(part.type().baryon_number()) * factor;
  ns_ += static_cast<double>(part.type().strangeness()) * factor;
}

Here is the call graph for this function:

void smash::ThermLatticeNode::add_particle_for_derivatives ( const ParticleData &  , double  , ThreeVector    )

inline

dummy function for update_lattice

Definition at line 67 of file grandcan_thermalizer.h.

{};

Here is the call graph for this function:

void smash::ThermLatticeNode::compute_rest_frame_quantities

(

HadronGasEos &

eos

)

Temperature, chemical potentials and rest frame velocity are calculated given the hadron gas equation of state object.

Parameters

[in]

eos

See also

HadronGasEos based on Tmu0, nb and ns

Returns

Temperature T, net baryon chemical potential mub, net strangeness chemical potential mus and the velocity of the Landau rest frame, under assumption that energy-momentum tensor has an ideal-fluid form. For more details and discussion see Oliinychenko:2015lva. The advantage of this rest frame transformation is that it conserves energy and momentum, even though the dissipative part of the energy-momentum tensor is neglected.

Todo:

(oliiny): use Newton's method instead of these iterations

Definition at line 40 of file grandcan_thermalizer.cc.

                                                                      {
  const int max_iter = 50;
  v_ = ThreeVector(0.0, 0.0, 0.0);
  double e_previous_step = 0.0;
  const double tolerance = 5.e-4;
  int iter;
  for (iter = 0; iter < max_iter; iter++) {
    e_previous_step = e_;
    e_ = Tmu0_.x0() - Tmu0_.threevec() * v_;
    if (std::abs(e_ - e_previous_step) < tolerance) {
      break;
    }
    const double gamma_inv = std::sqrt(1.0 - v_.sqr());
    EosTable::table_element tabulated;
    eos.from_table(tabulated, e_, gamma_inv * nb_);
    if (!eos.is_tabulated() || tabulated.p < 0.0) {
      auto T_mub_mus = eos.solve_eos(e_, gamma_inv * nb_, gamma_inv * ns_);
      T_ = T_mub_mus[0];
      mub_ = T_mub_mus[1];
      mus_ = T_mub_mus[2];
      p_ = HadronGasEos::pressure(T_, mub_, mus_);
    } else {
      p_ = tabulated.p;
      T_ = tabulated.T;
      mub_ = tabulated.mub;
      mus_ = tabulated.mus;
    }
    v_ = Tmu0_.threevec() / (Tmu0_.x0() + p_);
  }
  if (iter == max_iter) {
    std::cout << "Warning from solver: max iterations exceeded."
              << " Accuracy: " << std::abs(e_ - e_previous_step)
              << " is less than tolerance " << tolerance << std::endl;
  }
}

Here is the call graph for this function:

Here is the caller graph for this function:

void smash::ThermLatticeNode::set_rest_frame_quantities	(	double	T0,
		double	mub0,
		double	mus0,
		const ThreeVector	v0
	)

Set all the rest frame quantities to some values, this is useful for testing.

Parameters

[out]	T0	Rest frame temperature
[out]	mub0	Rest frame net baryon chemical potential
[out]	mus0	Rest frame net strangeness chemical potential
[out]	v0	Velocity of the rest frame

Definition at line 77 of file grandcan_thermalizer.cc.

                                                                       {
  T_ = T0;
  mub_ = mub0;
  mus_ = mus0;
  v_ = v0;
  e_ = HadronGasEos::energy_density(T_, mub_, mus_);
  p_ = HadronGasEos::pressure(T_, mub_, mus_);
  nb_ = HadronGasEos::net_baryon_density(T_, mub_, mus_);
  ns_ = HadronGasEos::net_strange_density(T_, mub_, mus_);
}

Here is the call graph for this function:

Here is the caller graph for this function:

FourVector smash::ThermLatticeNode::Tmu0 ( ) const

inline

Get Four-momentum flow of the cell.

Definition at line 92 of file grandcan_thermalizer.h.

{ return Tmu0_; }

Here is the caller graph for this function:

double smash::ThermLatticeNode::nb ( ) const

inline

Get net baryon density of the cell in the computational frame.

Definition at line 94 of file grandcan_thermalizer.h.

{ return nb_; }

Here is the caller graph for this function:

double smash::ThermLatticeNode::ns ( ) const

inline

Get net strangeness density of the cell in the computational frame.

Definition at line 96 of file grandcan_thermalizer.h.

{ return ns_; }

Here is the caller graph for this function:

double smash::ThermLatticeNode::e ( ) const

inline

Get energy density in the rest frame.

Definition at line 98 of file grandcan_thermalizer.h.

{ return e_; }

Here is the caller graph for this function:

double smash::ThermLatticeNode::p ( ) const

inline

Get pressure in the rest frame.

Definition at line 100 of file grandcan_thermalizer.h.

{ return p_; }

Here is the caller graph for this function:

ThreeVector smash::ThermLatticeNode::v ( ) const

inline

Get 3-velocity of the rest frame.

Definition at line 102 of file grandcan_thermalizer.h.

{ return v_; }

Here is the caller graph for this function:

double smash::ThermLatticeNode::T ( ) const

inline

Get the temperature.

Definition at line 104 of file grandcan_thermalizer.h.

{ return T_; }

Here is the caller graph for this function:

double smash::ThermLatticeNode::mub ( ) const

inline

Get the net baryon chemical potential.

Definition at line 106 of file grandcan_thermalizer.h.

{ return mub_; }

Here is the caller graph for this function:

double smash::ThermLatticeNode::mus ( ) const

inline

Get the net strangeness chemical potential.

Definition at line 108 of file grandcan_thermalizer.h.

{ return mus_; }

Here is the caller graph for this function:

Member Data Documentation

FourVector smash::ThermLatticeNode::Tmu0_

private

Four-momentum flow of the cell.

Definition at line 112 of file grandcan_thermalizer.h.

double smash::ThermLatticeNode::nb_

private

Net baryon density of the cell in the computational frame.

Definition at line 114 of file grandcan_thermalizer.h.

double smash::ThermLatticeNode::ns_

private

Net strangeness density of the cell in the computational frame.

Definition at line 116 of file grandcan_thermalizer.h.

double smash::ThermLatticeNode::e_

private

Energy density in the rest frame.

Definition at line 118 of file grandcan_thermalizer.h.

double smash::ThermLatticeNode::p_

private

Pressure in the rest frame.

Definition at line 120 of file grandcan_thermalizer.h.

ThreeVector smash::ThermLatticeNode::v_

private

Velocity of the rest frame.

Definition at line 122 of file grandcan_thermalizer.h.

double smash::ThermLatticeNode::T_

private

Temperature.

Definition at line 124 of file grandcan_thermalizer.h.

double smash::ThermLatticeNode::mub_

private

Net baryon chemical potential.

Definition at line 126 of file grandcan_thermalizer.h.

double smash::ThermLatticeNode::mus_

private

Net strangeness chemical potential.

Definition at line 128 of file grandcan_thermalizer.h.

---

The documentation for this class was generated from the following files:

• src/include/smash/grandcan_thermalizer.h
• src/grandcan_thermalizer.cc