hydro Namespace Reference

Items related to hydrodynamic systems. More...

## Namespaces

Solutions
Holds classes implementing common portions of solutions to various different (magneto)hydrodynamical systems.

Tags
Tags for hydrodynamic systems.

## Detailed Description

Items related to hydrodynamic systems.

## ◆ mass_flux() [1/2]

template<typename DataType , size_t Dim, typename Frame >
 tnsr::I hydro::mass_flux ( const Scalar< DataType > & rest_mass_density, const tnsr::I< DataType, Dim, Frame > & spatial_velocity, const Scalar< DataType > & lorentz_factor, const Scalar< DataType > & lapse, const tnsr::I< DataType, Dim, Frame > & shift, const Scalar< DataType > & sqrt_det_spatial_metric )
noexcept

Computes the vector $$J^i$$ in $$\dot{M} = -\int J^i s_i d^2S$$, representing the mass flux through a surface with normal $$s_i$$.

Note that the integral is understood as a flat-space integral: all metric factors are included in $$J^i$$. In particular, if the integral is done over a Strahlkorper, the StrahlkorperGr::euclidean_area_element of the Strahlkorper should be used, and $$s_i$$ is the normal one-form to the Strahlkorper normalized with the flat metric, $$s_is_j\delta^{ij}=1$$.

The formula is $$J^i = \rho W \sqrt{\gamma}(\alpha v^i-\beta^i)$$, where $$\rho$$ is the mass density, $$W$$ is the Lorentz factor, $$v^i$$ is the spatial velocity of the fluid, $$\gamma$$ is the determinant of the 3-metric $$\gamma_{ij}$$, $$\alpha$$ is the lapse, and $$\beta^i$$ is the shift.

## ◆ mass_flux() [2/2]

template<typename DataType , size_t Dim, typename Frame >
 void hydro::mass_flux ( gsl::not_null< tnsr::I< DataType, Dim, Frame > * > result, const Scalar< DataType > & rest_mass_density, const tnsr::I< DataType, Dim, Frame > & spatial_velocity, const Scalar< DataType > & lorentz_factor, const Scalar< DataType > & lapse, const tnsr::I< DataType, Dim, Frame > & shift, const Scalar< DataType > & sqrt_det_spatial_metric )
noexcept

Computes the vector $$J^i$$ in $$\dot{M} = -\int J^i s_i d^2S$$, representing the mass flux through a surface with normal $$s_i$$.

Note that the integral is understood as a flat-space integral: all metric factors are included in $$J^i$$. In particular, if the integral is done over a Strahlkorper, the StrahlkorperGr::euclidean_area_element of the Strahlkorper should be used, and $$s_i$$ is the normal one-form to the Strahlkorper normalized with the flat metric, $$s_is_j\delta^{ij}=1$$.

The formula is $$J^i = \rho W \sqrt{\gamma}(\alpha v^i-\beta^i)$$, where $$\rho$$ is the mass density, $$W$$ is the Lorentz factor, $$v^i$$ is the spatial velocity of the fluid, $$\gamma$$ is the determinant of the 3-metric $$\gamma_{ij}$$, $$\alpha$$ is the lapse, and $$\beta^i$$ is the shift.