Enzo-E Physics Config-Groups

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This section decribes the Physics subgroups that can be specified in the Physics Group of the parameter file. Each subgroup directly maps to a different type of Physics object in the codebase. These objects hold information that needs to be accessible across different Enzo-E methods.

"cosmology"

Specifies cosmological parameters

"fluid_props"

Specifies parameters related to the fluid properties. These parameters are largely into a few subcategories:

1. dual_energy: these parameters govern whether the simulation uses the dual-energy formalism and (if applicable) which formulation is used.

2. floors: these parameters specify floors for used for a small assortment of quantities.

3. eos: specifies parameters related to the (caloric) equation of state.

dual-energy formalism

A typical Godunov scheme might carry the specific total energy, \(E\), as one of its primary variables (the "total_energy" field). To compute the pressure (e.g. for reconstruction), the scheme needs to first compute the specific internal energy, \(e=p/((\gamma - 1) \rho)\), by subtracting the non-thermal energy components from \(E\). Numerical problems arise under extreme conditions when \(E_{\rm non-thermal}/e\) is extremely large (e.g. from some combination of high Mach number or magnetic energy) since \(e\) is the difference between 2 large numbers, \(E-E_{\rm non-thermal}\).

The dual-energy formalism is a technique used to avoid these numerical issues. Under this technique we track an additional field called "internal_energy" that we frequently synchronize with with the "total_energy" field. Under these extreme conditions, then use the "internal_energy" field to provide extra precision for \(e\).

In some sense the the dual-energy formalism can be considered an implementation detail of the hydro/MHD solver. However, the choice whether to use the dual-energy formalism has important implications for other methods and for initializers. This is the primary reason why the dual-energy formalism properties are tracked as part of the fluid_props physics object.

The relevant parameters are listed below:

Method fluid_props:dual_energy parameters

Parameter	Type	Default	Description
"type"	string	"disabled"	choice of formalism: "disabled", "bryan95", "modern"
"eta"	list(float)	-	Interpretation (and defaults) depend on value of "type"

When type is disabled, the simulation runs without the dual-energy formalism This is the default configuration and in this case, the eta parameter should NOT be specified.

The other two choices for type refer to two variants of the dual-energy formalism that we describe below.

"bryan95" variant

This is the original formulation of the dual-energy formalism described in Bryan et al (1995). It is used by the "ppm" solver and it is parameterized by two values: \(\eta_1\, \&\, \eta_2\).

fluid_props:dual_energy:eta expects a list of 2 entries: \([\eta_1, \eta_2]\) (users are NOT permitted to provide a single entry). When this parameter isn’t specified, it defaults to [0.001, 0.1].

"modern" variant

This implementation is used by the "mhd_vlct" solver and it more closely resembles the implementation employed in Enzo’s Runge–Kutta integrator than the "bryan95" variant. This variant is parameterized by a single value: \(eta\), and thus fluid_props:dual_energy:eta should only provide a single entry.

There are 3 primary differences from the "bryan95" variant:

1. the "internal_energy" field is always used to compute pressure. Under the bryan95 variant, pressure could be computed from "total_energy" or "internal_energy" (the decision was independent of synchronization).

2. pressure and "internal_energy" are not separately reconstructed. Instead, just the pressure is reconstructed. The "internal_energy" is computed at the left and right interfaces from the reconstructed quantities.

3. Synchronization of the total and internal energies is a local operation that doesn’t require knowledge of cell neighbors. The "bryan95" variant requires knowledge of the immediate neighbors (each synchronization incremented the stale depth - so 3 extra ghost zones would have been required for the "mhd_vlct" solver).

For clarity, the conditions for synchronization are provided below. The specific internal_energy, \(e\), is set to \(e'= E - (v^2 + B^2/\rho)/2\) (where \(E\) is the specific total_energy) when the following conditions are met:

• \(c_s'^2 > \eta v^2\), where \(c_s'^2=\gamma(\gamma - 1) e'\).

• \(c_s'^2 > \eta B^2/\rho\) (this is always satisfied in hydro mode)

• \(e' > e /2\)

If the above conditions are not met, then total_energy is set to \(e + (v^2 + B^2/\rho)/2\) in MHD mode (in hydro mode, it’s set to \(e + v^2/2\)).

Note: in the future, the behavior described in difference 2, may change to achieve better compatibility with Grackle.

AMR Inconsistency

A minor inconsistency is present in our simulation when we use either dual-energy formalism in AMR simulations. Each formulation of the dual-energy formalism requires the hydro-solver to add a source term to the "internal_energy" field. This source term involves the velocity on each cell face (just the component normal to the face). In practice, we compute the velocity in the Riemann Solver.

When neighboring cells compute the source term, they should theoretically use consistent values for the velocity component on the shared face. While this is true for neighbors with the same refinement level, it’s not true for neighbors with different refinement levels. In principle, a coarse cell should actually compute the source term from some kind of average of the velocity component on the faces of the neighboring finer cells (this could hypothetically be achieved with the equivalent of a “flux-correction”).

We don’t expect this inconsistency to be important given that the dual-energy formalism only affects highly supersonic flows and isn’t conservative anyway.

EOS

The "fluid_props:eos" subgroup holds parameters that configure the nominal (caloric) equation of state. These parameters primarily affect the Hydro/MHD methods and the "grackle" method. It also affects the calculation of pressure and temperature fields.

At this time, all simulations are assumed to have an ideal EOS and the only configurable parameter is provided below. In the future, further EOS customization will be supported in this section

Method fluid_props:eos parameters

Parameter	Type	Default	Description
"gamma"	float	5.0/3.0	Adiabatic index (a.k.a. the ratio of specific heats)

See Compatability with hydro/mhd solvers for further discussion about how the equation of state is handled when Method:grackle:primordial_chemistry > 1 (under these conditions Grackle models a spatially varying adiabatic index).

Floors

The "fluid_props:floors" subsection is used for specifying the floors of different fluid quantities. A list of the quantities whose floors can be configured are provided below.

Method fluid_props:floors parameters

Parameter	Type	Default	Description
"density"	float	-	The floor to apply to the "density" field.
"pressure"	float	-	The floor to apply to the "pressure" field.
"temperature"	float	-	The floor to apply to the "temperature" field.
"metallicity"	float	-	This multiplied by the "density" field and enzo_constants::metallicity_solar gives the floor for the "metal_density" field.

See Enzo-E Methods for discussions of the floors that are actually used by a given method. Be mindful that unlike the other parameters, the "metallicity" doesn’t directly specify the floor for a fluid field (the actual floor depends on other quantities).

Note

The "pressure" and "temperature" fields can be written to disk as derived quantities (if the fields are specified in the “derived” grouping). In these cases, these quantities are computed using EnzoComputePressure and EnzoComputeTemperature, respectively. You may want to check these classes to see if/when the floors get applied.