TimeDerivOfSpatialMetric.hpp
1 // Distributed under the MIT License.
2 // See LICENSE.txt for details.
3 
4 #pragma once
5 
6 #include <cstddef>
7 
9 #include "DataStructures/DataBox/Tag.hpp"
10 #include "DataStructures/DataVector.hpp"
12 #include "Evolution/Systems/GeneralizedHarmonic/Tags.hpp"
14 #include "PointwiseFunctions/GeneralRelativity/Tags.hpp"
15 #include "Utilities/ContainerHelpers.hpp"
16 #include "Utilities/Gsl.hpp"
17 #include "Utilities/TMPL.hpp"
18 
19 // IWYU pragma: no_forward_declare Tags::deriv
20 
21 /// \cond
22 namespace domain {
23 namespace Tags {
24 template <size_t Dim, typename Frame>
25 struct Coordinates;
26 } // namespace Tags
27 } // namespace domain
28 class DataVector;
29 template <typename X, typename Symm, typename IndexList>
30 class Tensor;
31 /// \endcond
32 
33 namespace GeneralizedHarmonic {
34 // @{
35 /*!
36  * \ingroup GeneralRelativityGroup
37  * \brief Computes time derivative of the spatial metric.
38  *
39  * \details Let the generalized harmonic conjugate momentum and spatial
40  * derivative variables be \f$\Pi_{ab} = -t^c \partial_c \psi_{ab} \f$ and
41  * \f$\Phi_{iab} = \partial_i \psi_{ab} \f$. As \f$ t_i \equiv 0 \f$. The time
42  * derivative of the spatial metric is given by the time derivative of the
43  * spatial sector of the spacetime metric, i.e.
44  * \f$ \partial_0 g_{ij} = \partial_0 \psi_{ij} \f$.
45  *
46  * To compute the latter, we use the evolution equation for \f$ \psi_{ij} \f$,
47  * c.f. eq.(35) of \cite Lindblom2005qh (with \f$\gamma_1 = -1\f$):
48  *
49  * \f[
50  * \partial_0 \psi_{ab} = - N \Pi_{ab} + N^k \Phi_{kab}
51  * \f]
52  */
53 template <size_t SpatialDim, typename Frame, typename DataType>
55  gsl::not_null<tnsr::ii<DataType, SpatialDim, Frame>*> dt_spatial_metric,
56  const Scalar<DataType>& lapse,
57  const tnsr::I<DataType, SpatialDim, Frame>& shift,
58  const tnsr::iaa<DataType, SpatialDim, Frame>& phi,
59  const tnsr::aa<DataType, SpatialDim, Frame>& pi) noexcept;
60 
61 template <size_t SpatialDim, typename Frame, typename DataType>
62 tnsr::ii<DataType, SpatialDim, Frame> time_deriv_of_spatial_metric(
63  const Scalar<DataType>& lapse,
64  const tnsr::I<DataType, SpatialDim, Frame>& shift,
65  const tnsr::iaa<DataType, SpatialDim, Frame>& phi,
66  const tnsr::aa<DataType, SpatialDim, Frame>& pi) noexcept;
67 // @}
68 
69 namespace Tags {
70 /*!
71  * \brief Compute item to get time derivative of the spatial metric from
72  * generalized harmonic and geometric variables
73  *
74  * \details See `time_deriv_of_spatial_metric()`. Can be retrieved using
75  * `gr::Tags::SpatialMetric` wrapped in `Tags::dt`.
76  */
77 template <size_t SpatialDim, typename Frame>
79  : ::Tags::dt<gr::Tags::SpatialMetric<SpatialDim, Frame, DataVector>>,
81  using argument_tags =
82  tmpl::list<gr::Tags::Lapse<DataVector>,
85 
86  using return_type = tnsr::ii<DataVector, SpatialDim, Frame>;
87 
88  static constexpr auto function = static_cast<void (*)(
90  const Scalar<DataVector>&, const tnsr::I<DataVector, SpatialDim, Frame>&,
91  const tnsr::iaa<DataVector, SpatialDim, Frame>&,
92  const tnsr::aa<DataVector, SpatialDim, Frame>&) noexcept>(
93  &time_deriv_of_spatial_metric<SpatialDim, Frame>);
94 
95  using base =
97 };
98 } // namespace Tags
99 } // namespace GeneralizedHarmonic
db::ComputeTag
Marks a DataBoxTag as being a compute item that executes a function.
Definition: Tag.hpp:109
GeneralizedHarmonic::pi
void pi(gsl::not_null< tnsr::aa< DataType, SpatialDim, Frame > * > pi, const Scalar< DataType > &lapse, const Scalar< DataType > &dt_lapse, const tnsr::I< DataType, SpatialDim, Frame > &shift, const tnsr::I< DataType, SpatialDim, Frame > &dt_shift, const tnsr::ii< DataType, SpatialDim, Frame > &spatial_metric, const tnsr::ii< DataType, SpatialDim, Frame > &dt_spatial_metric, const tnsr::iaa< DataType, SpatialDim, Frame > &phi) noexcept
Computes the conjugate momentum of the spacetime metric .
GeneralizedHarmonic::time_deriv_of_spatial_metric
void time_deriv_of_spatial_metric(gsl::not_null< tnsr::ii< DataType, SpatialDim, Frame > * > dt_spatial_metric, const Scalar< DataType > &lapse, const tnsr::I< DataType, SpatialDim, Frame > &shift, const tnsr::iaa< DataType, SpatialDim, Frame > &phi, const tnsr::aa< DataType, SpatialDim, Frame > &pi) noexcept
Computes time derivative of the spatial metric.
GeneralizedHarmonic
Items related to evolving the first-order generalized harmonic system.
Definition: Characteristics.cpp:21
gr::lapse
Scalar< DataType > lapse(const tnsr::I< DataType, SpatialDim, Frame > &shift, const tnsr::aa< DataType, SpatialDim, Frame > &spacetime_metric) noexcept
Compute lapse from shift and spacetime metric.
cstddef
GeneralizedHarmonic::Tags::Pi< SpatialDim, Frame >
DataVector
Stores a collection of function values.
Definition: DataVector.hpp:42
GeneralizedHarmonic::phi
void phi(gsl::not_null< tnsr::iaa< DataType, SpatialDim, Frame > * > phi, const Scalar< DataType > &lapse, const tnsr::i< DataType, SpatialDim, Frame > &deriv_lapse, const tnsr::I< DataType, SpatialDim, Frame > &shift, const tnsr::iJ< DataType, SpatialDim, Frame > &deriv_shift, const tnsr::ii< DataType, SpatialDim, Frame > &spatial_metric, const tnsr::ijj< DataType, SpatialDim, Frame > &deriv_spatial_metric) noexcept
Computes the auxiliary variable used by the generalized harmonic formulation of Einstein's equations...
gr::Tags::Shift
Definition: Tags.hpp:48
gr::shift
tnsr::I< DataType, SpatialDim, Frame > shift(const tnsr::aa< DataType, SpatialDim, Frame > &spacetime_metric, const tnsr::II< DataType, SpatialDim, Frame > &inverse_spatial_metric) noexcept
Compute shift from spacetime metric and inverse spatial metric.
GeneralizedHarmonic::Tags::Phi< SpatialDim, Frame >
Tags::dt
Prefix indicating a time derivative.
Definition: Prefixes.hpp:29
GeneralizedHarmonic::Tags::TimeDerivSpatialMetricCompute
Compute item to get time derivative of the spatial metric from generalized harmonic and geometric var...
Definition: TimeDerivOfSpatialMetric.hpp:78
Scalar
Tensor< T, Symmetry<>, index_list<> > Scalar
Definition: TypeAliases.hpp:21
Gsl.hpp
Tensor.hpp
PartialDerivatives.hpp
Prefixes.hpp
TMPL.hpp
gsl::not_null
Require a pointer to not be a nullptr
Definition: Gsl.hpp:183