BnsInitialData Namespace Reference

Items related to solving for irrotational Binary Neutron Star initial data. More...

Namespaces
namespace	BoundaryConditions
	Boundary conditions for binary neutron star initial data.
namespace	Tags
	Items related to solving for irrotational bns initial data.

Classes
struct	FirstOrderSystem
	The Irrotational Bns equations From Baumgarte and Shapiro Chapter 15 formulated as a set of coupled first-order PDEs. More...
struct	Fluxes
	Compute the fluxes \(F^i\) for the curved-space Irrotatational BNS equations on a spatial metric \(\gamma_{ij}\). More...
struct	Sources
	Add the sources \(S_A\) for the curved-space Irrotatioanl BNS equation on a spatial metric \(\gamma_{ij}\). More...

Functions
void	fluxes_on_face (gsl::not_null< tnsr::I< DataVector, 3 > * > face_flux_for_potential, const tnsr::i< DataVector, 3 > &face_normal, const tnsr::I< DataVector, 3 > &face_normal_vector, const tnsr::II< DataVector, 3 > &rotational_shift_stress, const Scalar< DataVector > &velocity_potential)
	Compute the fluxes. More...
void	potential_fluxes (gsl::not_null< tnsr::I< DataVector, 3 > * > flux_for_potential, const tnsr::II< DataVector, 3 > &rotational_shift_stress, const tnsr::II< DataVector, 3 > &inverse_spatial_metric, const tnsr::i< DataVector, 3 > &velocity_potential_gradient)
	Compute the generic fluxes \( F^i = D^i \Phi - \frac{B^jD_j\Phi}{\alpha^2} B^i \) for the Irrotational BNS equation for the velocity potential.
void	add_potential_sources (gsl::not_null< Scalar< DataVector > * > source_for_potential, const tnsr::i< DataVector, 3 > &log_deriv_lapse_times_density_over_specific_enthalpy, const tnsr::i< DataVector, 3 > &christoffel_contracted, const tnsr::I< DataVector, 3 > &flux_for_potential)
	Add the sources \(S=-\Gamma^i_{ij}F^j - \D_j \left(\ln\alpha \rho / h\right) F^j\) for the curved-space Irrotational BNS equation on a spatial metric \(\gamma_{ij}\). More...

Detailed Description

Items related to solving for irrotational Binary Neutron Star initial data.

We solve the equations for the relativistic quasi-equilibrium configuration associated with an object in a quasi-circular orbit around a binary companion. We assume the compact object is nonspinning, which allows the solution to be written in terms of a "velocity potential", which is a function \(\Phi\) such that \(D_i \Phi = \rho h u_i\), with \( \rho, h\) the rest mass density and specific enthalpy respectively, and \(u_i \) the spatial part of the four velocity

Function Documentation

add_potential_sources()

void BnsInitialData::add_potential_sources	(	gsl::not_null< Scalar< DataVector > * >	source_for_potential,
		const tnsr::i< DataVector, 3 > &	log_deriv_lapse_times_density_over_specific_enthalpy,
		const tnsr::i< DataVector, 3 > &	christoffel_contracted,
		const tnsr::I< DataVector, 3 > &	flux_for_potential
	)

Add the sources \(S=-\Gamma^i_{ij}F^j - \D_j \left(\ln\alpha \rho / h\right) F^j\) for the curved-space Irrotational BNS equation on a spatial metric \(\gamma_{ij}\).

These sources arise from the non-principal part of the Laplacian on a non-Euclidean background.

fluxes_on_face()

void BnsInitialData::fluxes_on_face	(	gsl::not_null< tnsr::I< DataVector, 3 > * >	face_flux_for_potential,
		const tnsr::i< DataVector, 3 > &	face_normal,
		const tnsr::I< DataVector, 3 > &	face_normal_vector,
		const tnsr::II< DataVector, 3 > &	rotational_shift_stress,
		const Scalar< DataVector > &	velocity_potential
	)

Compute the fluxes.

\[ F^i = \gamma^{ij} n_j \Phi - n_j \Phi \frac{B^iB^j}{\alpha^2} \]

where \( n_j\) is the face_normal.

The face_normal_vector is \( \gamma^{ij} n_j\).