Fix conservative variables using method developed by Foucart. More...

#include <FixConservatives.hpp>

Classes
struct	CutoffD
	Cutoff below which $D = ρ W$ is set to MinimumValueOfD. More...

struct	CutoffYe
	Cutoff below which $Y_{e}$ is set to MinimumValueOfYe. More...

struct	Enable
	Whether or not the limiting is enabled. More...

struct	MagneticField
	How to treat the magnetic field. More...

struct	MinimumValueOfD
	Minimum value of rest-mass density times lorentz factor. More...

struct	MinimumValueOfYe
	Minimum value of electron fraction $Y_{e}$ . More...

struct	SafetyFactorForB
	Safety factor $ϵ_{B}$ . More...

struct	SafetyFactorForS
	Safety factor $ϵ_{S}$ . More...

struct	SafetyFactorForSCutoffD
	Cutoff in $ρ_{0} W$ below which we use a stricter safety factor for the magnitude of S. More...

struct	SafetyFactorForSSlope
	Below SafetyFactorForSCutoffD, reduce $ϵ_{S}$ by SafetyFactorForSSlope times $\log_{10} (ρ_{0} W / S a f e t y F a c t o r F o r S C u t o f f D)$ . More...

Public Types
using	options = implementation defined

using	return_tags = implementation defined

using	argument_tags = implementation defined

Public Member Functions
	FixConservatives (double minimum_rest_mass_density_times_lorentz_factor, double rest_mass_density_times_lorentz_factor_cutoff, double minimum_electron_fraction, double electron_fraction_cutoff, double safety_factor_for_magnetic_field, double safety_factor_for_momentum_density, double safety_factor_for_momentum_density_cutoff_d, double safety_factor_for_momentum_density_slope, bool enable, hydro::MagneticFieldTreatment magnetic_field_treatment, const Options::Context &context={})

	FixConservatives (const FixConservatives &)=default

FixConservatives &	operator= (const FixConservatives &)=default

	FixConservatives (FixConservatives &&)=default

FixConservatives &	operator= (FixConservatives &&)=default

void	pup (PUP::er &p)

bool	operator() (gsl::not_null< Scalar< DataVector > * > tilde_d, gsl::not_null< Scalar< DataVector > * > tilde_ye, 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
	Returns `true` if any variables were fixed.

Static Public Attributes
static constexpr Options::String	help

Friends
bool	operator== (const FixConservatives &lhs, const FixConservatives &rhs)

Detailed Description

Fix conservative variables using method developed by Foucart.

Adjusts the conservative variables as follows:

If the electron fraction $Y_{e}$ is below the value of the option CutoffYe, change ${\tilde{Y}}_{e}$ to $\tilde{D}$ times the value of the option MinimumValueOfYe.
Changes $\tilde{D}$ , the generalized mass-energy density, such that $D$ , the product of the rest mass density $ρ$ and the Lorentz factor $W$ , is set to value of the option MinimumValueOfD, whenever $D$ is below the value of the option CutoffD.
Increases $\tilde{τ}$ , the generalized internal energy density, such that ${\tilde{B}}^{2} \leq 2 \sqrt{γ} (1 - ϵ_{B}) \tilde{τ}$ , where ${\tilde{B}}^{i}$ is the generalized magnetic field, $γ$ is the determinant of the spatial metric, and $ϵ_{B}$ is the option SafetyFactorForB.
Decreases ${\tilde{S}}_{i}$ , the generalized momentum density, such that ${\tilde{S}}^{2} \leq (1 - ϵ_{S}) {\tilde{S}}_{m a x}^{2}$ , where $ϵ_{S}$ is the option SafetyFactorForS, and ${\tilde{S}}_{m a x}^{2}$ 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()

Member Data Documentation

◆ help

constexpr Options::String grmhd::ValenciaDivClean::FixConservatives::help

staticconstexpr

Initial value:

= {

"Variable fixing used in Foucart's thesis.\n"}

The documentation for this class was generated from the following file:

src/Evolution/Systems/GrMhd/ValenciaDivClean/FixConservatives.hpp

Classes

Public Types

Public Member Functions

Static Public Attributes

Friends

Detailed Description

Member Data Documentation

◆ help