Fluxes.hpp

// Distributed under the MIT License.
// See LICENSE.txt for details.

#pragma once

#include <cstddef>

#include "DataStructures/Tensor/TypeAliases.hpp"  // IWYU pragma: keep

/// \cond
namespace gsl {
template <typename T>
class not_null;
}  // namespace gsl

class DataVector;
/// \endcond

// IWYU pragma: no_forward_declare Tensor

namespace RelativisticEuler {
namespace Valencia {

/*!
 * \brief The fluxes of the conservative variables
 *
 * \f{align*}
 * F^i({\tilde D}) = &~ {\tilde D} v^i_{tr} \\
 * F^i({\tilde S}_j) = &~  {\tilde S}_j v^i_{tr} + \sqrt{\gamma} \alpha p
 * \delta^i_j \\
 * F^i({\tilde \tau}) = &~  {\tilde \tau} v^i_{tr} + \sqrt{\gamma} \alpha p v^i
 * \f}
 * where the conservative variables \f${\tilde D}\f$, \f${\tilde S}_i\f$, and
 * \f${\tilde \tau}\f$ are a generalized mass-energy density, momentum density,
 * and specific internal energy density as measured by an Eulerian observer,
 * \f$v^i_{tr} = \alpha v^i - \beta^i\f$ is the transport velocity, \f$\alpha\f$
 * is the lapse, \f$\beta^i\f$ is the shift, \f$v^i\f$ is the spatial velocity,
 * \f$\gamma\f$ is the determinant of the spatial metric, and \f$p\f$ is the
 * pressure.
 */
template <size_t Dim>
void fluxes(
    gsl::not_null<tnsr::I<DataVector, Dim, Frame::Inertial>*> tilde_d_flux,
    gsl::not_null<tnsr::I<DataVector, Dim, Frame::Inertial>*> tilde_tau_flux,
    gsl::not_null<tnsr::Ij<DataVector, Dim, Frame::Inertial>*> tilde_s_flux,
    const Scalar<DataVector>& tilde_d, const Scalar<DataVector>& tilde_tau,
    const tnsr::i<DataVector, Dim, Frame::Inertial>& tilde_s,
    const Scalar<DataVector>& lapse,
    const tnsr::I<DataVector, Dim, Frame::Inertial>& shift,
    const Scalar<DataVector>& sqrt_det_spatial_metric,
    const Scalar<DataVector>& pressure,
    const tnsr::I<DataVector, Dim, Frame::Inertial>& spatial_velocity) noexcept;
}  // namespace Valencia
}  // namespace RelativisticEuler