We need to compute ADM quantities in our initial data sets to understand the physical properties of the data that we're evolving. To learn about ADM quantities, a good place to start is chapter 3.5 in the book "Numerical Relativity" by Baumgarte & Shapiro. For example, we want to compute M_ADM by Eq. (3.149) in the book. It involves a surface integral over the excision boundaries that represent the two black holes, and a volume integral over the rest of the domain. First steps are:
Write functions that compute the integrands of Eq. (3.149). They can go in src/PointwiseFunctions/Xcts/Adm.{h,c}pp. The volume integrand function can look like this:
We can use tensor expressions to compute quantities. Search for tenex::evaluate in the code to find examples. We can take derivatives using the partial_derivative function from NumericalAlgorithms/LinearOperators/PartialDerivatives.hpp.
Test the functions by computing the ADM mass of a Schwarzschild black hole in Kerr-Schild coordinates. This can be written in tests/Unit/PointwiseFunctions/Xcts/Test_Adm.cpp.
Write compute tags for both integrands and add them to the SolveXcts executable.
Observe the volume integral using the ObserveVolumeIntegrals event and the surface integral using the excision surface observer.
Then we can compute also ADM momentum and angular momentum. See also http://arxiv.org/abs/1506.01689 for what SpEC does for those.
nilsvu
commented
1 year ago
We need to compute ADM quantities in our initial data sets to understand the physical properties of the data that we're evolving. To learn about ADM quantities, a good place to start is chapter 3.5 in the book "Numerical Relativity" by Baumgarte & Shapiro. For example, we want to compute M_ADM by Eq. (3.149) in the book. It involves a surface integral over the excision boundaries that represent the two black holes, and a volume integral over the rest of the domain. First steps are:
Write functions that compute the integrands of Eq. (3.149). They can go in
src/PointwiseFunctions/Xcts/Adm.{h,c}pp. The volume integrand function can look like this:We can use tensor expressions to compute quantities. Search for
tenex::evaluatein the code to find examples. We can take derivatives using thepartial_derivativefunction fromNumericalAlgorithms/LinearOperators/PartialDerivatives.hpp.Test the functions by computing the ADM mass of a Schwarzschild black hole in Kerr-Schild coordinates. This can be written in
tests/Unit/PointwiseFunctions/Xcts/Test_Adm.cpp.Write compute tags for both integrands and add them to the
SolveXctsexecutable.Observe the volume integral using the
ObserveVolumeIntegralsevent and the surface integral using the excision surface observer.Then we can compute also ADM momentum and angular momentum. See also http://arxiv.org/abs/1506.01689 for what SpEC does for those.