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SpECTRE
2021.08.02
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Items related to hydrodynamic systems. More...
Namespaces | |
| namespace | Solutions |
| Holds classes implementing common portions of solutions to various different (magneto)hydrodynamical systems. | |
| namespace | Tags |
| Tags for hydrodynamic systems. | |
Functions | |
| template<typename DataType , size_t Dim, typename Frame > | |
| void | lorentz_factor (gsl::not_null< Scalar< DataType > * > result, const tnsr::I< DataType, Dim, Frame > &spatial_velocity, const tnsr::i< DataType, Dim, Frame > &spatial_velocity_form) noexcept |
| Computes the Lorentz factor \(W=1/\sqrt{1 - v^i v_i}\). | |
| template<typename DataType , size_t Dim, typename Frame > | |
| Scalar< DataType > | lorentz_factor (const tnsr::I< DataType, Dim, Frame > &spatial_velocity, const tnsr::i< DataType, Dim, Frame > &spatial_velocity_form) noexcept |
| Computes the Lorentz factor \(W=1/\sqrt{1 - v^i v_i}\). | |
| template<typename DataType > | |
| void | lorentz_factor (gsl::not_null< Scalar< DataType > * > result, const Scalar< DataType > &spatial_velocity_squared) noexcept |
| Computes the Lorentz factor \(W=1/\sqrt{1 - v^i v_i}\). | |
| template<typename DataType > | |
| Scalar< DataType > | lorentz_factor (const Scalar< DataType > &spatial_velocity_squared) noexcept |
| Computes the Lorentz factor \(W=1/\sqrt{1 - v^i v_i}\). | |
| template<typename DataType , size_t Dim, typename Frame > | |
| void | 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 \(s_i\). More... | |
| template<typename DataType , size_t Dim, typename Frame > | |
| tnsr::I< DataType, Dim, Frame > | 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 \(s_i\). More... | |
| template<typename DataType , size_t ThermodynamicDim> | |
| void | sound_speed_squared (gsl::not_null< Scalar< DataType > * > result, const Scalar< DataType > &rest_mass_density, const Scalar< DataType > &specific_internal_energy, const Scalar< DataType > &specific_enthalpy, const EquationsOfState::EquationOfState< true, ThermodynamicDim > &equation_of_state) noexcept |
| Computes the relativistic sound speed squared. More... | |
| template<typename DataType , size_t ThermodynamicDim> | |
| Scalar< DataType > | sound_speed_squared (const Scalar< DataType > &rest_mass_density, const Scalar< DataType > &specific_internal_energy, const Scalar< DataType > &specific_enthalpy, const EquationsOfState::EquationOfState< true, ThermodynamicDim > &equation_of_state) noexcept |
| Computes the relativistic sound speed squared. More... | |
| template<typename DataType > | |
| void | relativistic_specific_enthalpy (gsl::not_null< Scalar< DataType > * > result, const Scalar< DataType > &rest_mass_density, const Scalar< DataType > &specific_internal_energy, const Scalar< DataType > &pressure) noexcept |
| Computes the relativistic specific enthalpy \(h\) as: \( h = 1 + \epsilon + \frac{p}{\rho} \) where \(\epsilon\) is the specific internal energy, \(p\) is the pressure, and \(\rho\) is the rest mass density. | |
| template<typename DataType > | |
| Scalar< DataType > | relativistic_specific_enthalpy (const Scalar< DataType > &rest_mass_density, const Scalar< DataType > &specific_internal_energy, const Scalar< DataType > &pressure) noexcept |
| Computes the relativistic specific enthalpy \(h\) as: \( h = 1 + \epsilon + \frac{p}{\rho} \) where \(\epsilon\) is the specific internal energy, \(p\) is the pressure, and \(\rho\) is the rest mass density. | |
Items related to hydrodynamic systems.
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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.
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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.