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SpECTRE
v2024.09.29
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Control error in the Shape coordinate map. More...
#include <Shape.hpp>
Public Types | |
| using | object_centers = domain::object_list< Horizon > |
| using | options = tmpl::list<> |
Public Member Functions | |
| void | pup (PUP::er &) |
| template<typename Metavariables , typename... TupleTags> | |
| DataVector | operator() (const ::TimescaleTuner< true > &, const Parallel::GlobalCache< Metavariables > &cache, const double time, const std::string &function_of_time_name, const tuples::TaggedTuple< TupleTags... > &measurements) |
Static Public Attributes | |
| static constexpr Options::String | help |
Control error in the Shape coordinate map.
Computes the error for each \( l,m \) mode of the shape map except for \( l=0 \) and \( l=1 \). This is because the \( l=0 \) mode is controlled by characteristic speed control, and the \( l=1 \) mode is redundant with the Translation map. The equation for the control error is Eq. (77) from [88] which is
\begin{align} Q_{lm} &= -\frac{r_\mathrm{EB} - Y_{00}\lambda_{00}(t)}{\sqrt{\frac{\pi}{2}} Y_{00}S_{00}} S_{lm} - \lambda_{lm}(t), \quad l>=2 \label{eq:shape_control_error} \end{align}
where \( r_\mathrm{EB} \) is the radius of the excision boundary in the grid frame, \( \lambda_{00}(t) \) is the size map parameter, \( \lambda_{lm}(t) \) for \( l>=2 \) are the shape map parameters, and \( S_{lm}\) are the coefficients of the harmonic expansion of the apparent horizon. The coefficients \( \lambda_{lm}(t) \) (not including \( l=0 \)) and \( S_{lm}\) (including \( l=0 \)) are stored as the real-valued coefficients \( a_{lm} \) and \( b_{lm} \) of the SPHEREPACK spherical-harmonic expansion (in ylm::Spherepack). The \(\lambda_{00}(t)\) coefficient, on the other hand, is stored as the complex coefficient \( A_{00} \) of the standard \( Y_{lm} \) decomposition. Because \( a_{00} = \sqrt{\frac{2}{\pi}}A_{00} \), there is an extra factor of \( \sqrt{\frac{\pi}{2}} \) in the above formula in the denominator of the fraction multiplying the \( S_{00}\) component so it is represented in the \( Y_{lm} \) decomposition just like \( r_{EB} \) and \( \lambda_{00} \) are). That way, we ensure the numerator and denominator are represented in the same way before we take their ratio.
Requirements:
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staticconstexpr |