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| FixConservatives (double minimum_rest_mass_density_times_lorentz_factor, double rest_mass_density_times_lorentz_factor_cutoff, double safety_factor_for_magnetic_field, double safety_factor_for_momentum_density, const Options::Context &context={}) |
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| FixConservatives (const FixConservatives &)=default |
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FixConservatives & | operator= (const FixConservatives &)=default |
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| FixConservatives (FixConservatives &&) noexcept=default |
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FixConservatives & | operator= (FixConservatives &&) noexcept=default |
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void | pup (PUP::er &p) noexcept |
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bool | operator() (gsl::not_null< Scalar< DataVector > * > tilde_d, gsl::not_null< Scalar< DataVector > * > tilde_tau, gsl::not_null< tnsr::i< DataVector, 3, Frame::Inertial > * > tilde_s, const tnsr::I< DataVector, 3, Frame::Inertial > &tilde_b, const tnsr::ii< DataVector, 3, Frame::Inertial > &spatial_metric, const tnsr::II< DataVector, 3, Frame::Inertial > &inv_spatial_metric, const Scalar< DataVector > &sqrt_det_spatial_metric) const noexcept |
| | Returns true if any variables were fixed.
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Fix conservative variables using method developed by Foucart.
Adjusts the conservative variables as follows:
- Changes \({\tilde D}\), the generalized mass-energy density, such that \(D\), the product of the rest mass density \(\rho\) and the Lorentz factor \(W\), is set to value of the option
MinimumValueOfD, whenever \(D\) is below the value of the option CutoffD.
- Increases \({\tilde \tau}\), the generalized internal energy density, such that \({\tilde B}^2 \leq 2 \sqrt{\gamma} (1 - \epsilon_B) {\tilde \tau}\), where \({\tilde B}^i\) is the generalized magnetic field, \(\gamma\) is the determinant of the spatial metric, and \(\epsilon_B\) is the option
SafetyFactorForB.
- Decreases \({\tilde S}_i\), the generalized momentum density, such that \({\tilde S}^2 \leq (1 - \epsilon_S) {\tilde S}^2_{max}\), where \(\epsilon_S\) is the option
SafetyFactorForS, and \({\tilde S}^2_{max}\) is a complicated function of the conservative variables which can only be found through root finding. There are sufficient conditions for a set of conservative variables to satisfy the inequality, which can be used to avoid root finding at most points.
- Note
- The routine currently assumes the minimum specific enthalpy is one.
For more details see Appendix B from the thesis of Francois Foucart
You can plot the function whose root we are finding using:
import numpy as np
import matplotlib.pyplot as plt
upper_bound = 1.000119047987896748e+00
lower_bound = 1.000000000000000000e+00
s_tilde_squared = 5.513009056734747750e-30
d_tilde = 1.131468709980503465e-12
sqrt_det_g: 1.131468709980503418e+00
tau_tilde = 1.346990732914080573e-16
b_tilde_squared = 3.048155733848927391e-16
b_squared_over_d = 2.380959757934347320e-04
tau_over_d = 1.190479878968363843e-04
normalized_s_dot_b = -9.999999082462245337e-01
def function_of_w(lorentz_factor):
return ((lorentz_factor + b_squared_over_d - tau_over_d - 1.0) *
(lorentz_factor**2 + b_squared_over_d * normalized_s_dot_b**2 *
(b_squared_over_d + 2.0 * lorentz_factor)) -
0.5 * b_squared_over_d -
0.5 * b_squared_over_d * normalized_s_dot_b**2 *
(lorentz_factor**2 - 1.0 +
2.0 * lorentz_factor * b_squared_over_d + b_squared_over_d**2))
lorentz_factor = np.linspace(lower_bound, upper_bound, num=10000)
plt.plot(lorentz_factor, function_of_w(lorentz_factor))
plt.show()