VariableFixing::FixToAtmosphere< Dim >::KappaLimitingOptions Struct Reference

Options for limiting the temperature in the atmosphere by effectively limiting the polytropic constant, with a generalization for finite temperature equations of state. More...

#include <FixToAtmosphere.hpp>

Classes
struct	DensityLowerBound
struct	DensityUpperBound
struct	EplisonKappaMinus
struct	EpsilonKappaMax
struct	LimitAboveDensityUpperBound
struct	MinTemperature

Public Types
using	options = implementation defined

Public Member Functions
void	pup (PUP::er &p)
bool	operator== (const KappaLimitingOptions &rhs) const
bool	operator!= (const KappaLimitingOptions &rhs) const

Public Attributes
double	density_lower_bound {std::numeric_limits<double>::signaling_NaN()}
double	eplison_kappa_minus {std::numeric_limits<double>::signaling_NaN()}
double	density_upper_bound {std::numeric_limits<double>::signaling_NaN()}
double	epsilon_kappa_max {std::numeric_limits<double>::signaling_NaN()}
std::optional< double >	min_temperature {std::nullopt}
bool	limit_above_density_upper_bound {false}

Static Public Attributes
static constexpr Options::String	help

Detailed Description

template<size_t Dim>
struct VariableFixing::FixToAtmosphere< Dim >::KappaLimitingOptions

Options for limiting the temperature in the atmosphere by effectively limiting the polytropic constant, with a generalization for finite temperature equations of state.

The basic density limit is fine for a cold EOS, but when a finite temperature EOS is used the temperature needs to be controlled in the atmosphere. While the basic bound of $T\in [T_{\mathrm{m}\mathrm{i}\mathrm{n}},T_{\mathrm{m}\mathrm{a}\mathrm{x}}]$ is a necessary condition, it is often not sufficient for stability in the atmosphere. We define lower and upper bounds ${\rho }_{{\tau }_{-}}$ and ${\rho }_{{\tau }_{+}}$ for $\rho$ where we apply different limiting behavior when $\rho <{\rho }_{{\tau }_{-}}$, $\rho \in [{\rho }_{{\tau }_{-}},{\rho }_{{\tau }_{+}}]$, and $\rho >{\rho }_{{\tau }_{+}}$.

When $\rho <{\rho }_{{\tau }_{-}}$ we set $T=T_{\mathrm{m}\mathrm{i}\mathrm{n}}$ if $|T-T_{\mathrm{m}\mathrm{i}\mathrm{n}}|<{ϵ}_{{\kappa }_{-}}|T|$, otherwise we don't change $T$. SpEC uses ${ϵ}_{{\kappa }_{-}}={10}^{-3}$.

When $\rho \in [{\rho }_{{\tau }_{-}},{\rho }_{{\tau }_{+}}]$ we apply a more complicated algorithm. We define

$$\begin{array}{r}{\kappa }_{\mathrm{m}\mathrm{a}\mathrm{x}}=1+{ϵ}_{\kappa ,\mathrm{m}\mathrm{a}\mathrm{x}}min(\frac{\rho -{\rho }_{{\tau }_{-}}}{{\rho }_{{\tau }_{+}}-{\rho }_{{\tau }_{-}}},1)\end{array}$$

where ${ϵ}_{\kappa ,\mathrm{m}\mathrm{a}\mathrm{x}}\ge 0$ (set to 0.01 in SpEC). With ${\kappa }_{\mathrm{m}\mathrm{a}\mathrm{x}}$ computed we now limit the temperature. We define $p_{\mathrm{m}\mathrm{i}\mathrm{n}}=p(\rho ,T_{\mathrm{m}\mathrm{i}\mathrm{n}},Y_e)$, $p=p(\rho ,T,Y_e)$, and $p_{{\kappa }_{\mathrm{m}\mathrm{a}\mathrm{x}}}=p_{\mathrm{m}\mathrm{i}\mathrm{n}}{\kappa }_{\mathrm{m}\mathrm{a}\mathrm{x}}$. We then need to find $T$ such that $p(\rho ,T,Y_e)=p_{{\kappa }_{\mathrm{m}\mathrm{a}\mathrm{x}}}$. We do this by finding the root of

$$\begin{array}{r}f(T^{\prime })=p(\rho ,T^{\prime },Y_e)-p_{{\kappa }_{\mathrm{m}\mathrm{a}\mathrm{x}}}.\end{array}$$

We bracket the temperature $T^{\prime }\in [T_{min},T]$, where $T$ is the unmodified temperature. We solve the equation using the TOMS748 algorithm to avoid the need for derivatives of the pressure with respect to the temperature. If $T-T_{min}<{10}^{-13}$ we set $T^{\prime }=\frac{1}{2}(T+T_{min})$ to avoid any root find.

When $\rho >{\rho }_{{\tau }_{+}}$ we optionally can apply the same procedure as in the previous case, but with ${\kappa }_{\mathrm{m}\mathrm{a}\mathrm{x}}=1+{ϵ}_{\kappa ,\mathrm{m}\mathrm{a}\mathrm{x}}$. This is not typically done.

Member Data Documentation

help

template<size_t Dim>

constexpr Options::String VariableFixing::FixToAtmosphere< Dim >::KappaLimitingOptions::help

staticconstexpr

Initial value:

= {
        "If set then we apply a limiting precodure on the temperature near the "
        "atmosphere based on essentially limiting the polytropic constant in a "
        "Gamma-law equation of state."}

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

• src/Evolution/VariableFixing/FixToAtmosphere.hpp