SpECTRE  v2024.06.18
BnsInitialData Namespace Reference

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

## Namespaces

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 $$F^i = D^i \Phi - B^jD_j\Phi /\alpha^2 B^i$$ 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 $$S=-\Gamma^i_{ij}F^j - \D_j \left(\alpha \rho / h\right) F^j$$ 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

 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 $$S=-\Gamma^i_{ij}F^j - \D_j \left(\alpha \rho / h\right) F^j$$ 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 $$\gamma^{ij} n_j$$.