2008-04-07

Abstract

Provide grid functions for the stress-energy tensor ${T}_{\mu \nu}$, and schedule when these grid functions are calculated. This allows different thorns to cooperate without explicitly depending on each other. Thorn TmunuBase is for the stress-energy tensor what thorn ADMBase is for the metric tensor.

Thorn TmunuBase provides core infrastructure for thorns implementing some kind of energy or matter in general relativity, for example general relativistic hydrodynamics formulations. It provides the basic variables, i.e., the stress-energy tensor ${T}_{\mu \nu}$, in addition to a set of parameters to regulate their use. These variables are used to communicate between (possibly multiple) thorns contributing to the stress-energy content of the spacetime, and thorns needing to evaluate the stress-energy tensor such as spacetime evolution methods. It also provides schedule groups to manage when ${T}_{\mu \nu}$ is calculated and when it is ready for access.

TmunuBase weakly assumes (but does not require) that the spacetime is described in terms of a $3+1$ decomposition. The variables provided by TmunuBase are:

- The “scalar” part of ${T}_{\mu \nu}$, its time-time component: eTtt
- The “vector” part of ${T}_{\mu \nu}$, its time-space components: eTtx, eTty, eTtz
- The “tensor” part of ${T}_{\mu \nu}$, its space-space components: eTxx, eTxy, eTxz, eTyy, eTyz, eTzz

These components have the prefix e to avoid naming conflicts with existing variables. Many thorns dealing with matter already use variable names such as Ttt.

These variables have up to three time levels.

By default, the TmunuBase variables have no storage, and TmunuBase is inactive. This makes it possible to add a matter interface to existing vacuum spacetime methods without changing their behaviour.

Several parameters choose how TmunuBase behaves at run time:

- The parameter stress_energy_storage activates storage for ${T}_{\mu \nu}$ and enables the schedule groups which calculate it.
- The parameter stress_energy_at_RHS moves calculating the ${T}_{\mu \nu}$
from the evol bin into the MoL_PostStep group. This increases the order of accuracy of the
spacetime–matter coupling, but is only possible when thorn MoL is used.
^{1}Generally, this parameter should be set when MoL is used. - The parameter timelevels chooses the number of time levels for ${T}_{\mu \nu}$. The default is a single time level, which is sufficient for unigrid simulation. Mesh refinement simulation may require several time levels if mesh refinement boundaries require correct values.
- The parameter prolongation_type defines the prolongation operator for mesh refinement boundaries. The default is Lagrange interpolation.

The grid scalar stress_energy_state describes whether the ${T}_{\mu \nu}$ variables have storage.

There may be multiple thorns contributing to ${T}_{\mu \nu}$. Therefore, thorn TmunuBase initialises ${T}_{\mu \nu}$ to zero, and each thorn has to add to the existing values in ${T}_{\mu \nu}$. The corresponding routine should be scheduled in the bin AddToTmunu. Note: Do not schedule anything in the schedule bin SetTmunu.

Since the values of ${T}_{\mu \nu}$ change at each time step, or – if a thorn like MoL is used – at each substep, ${T}_{\mu \nu}$ needs to be recalculated frequently. This happens either in the schedule bin evol or in the schedule group MoL_PostStep. ${T}_{\mu \nu}$ may only be accessed after it has been calculated, e.g. IN MoL_PostStep AFTER SetTmunu. ${T}_{\mu \nu}$ can be freely accessed at other times, e.g. in MoL_CalcRHS or at poststep or analyisis.

We thank I. Hawke for designing and implementing thorn MoL, without which a generic high-order coupling between spacetime and hydrodynamics methods would not be possible.

prolongation_type | Scope: private | STRING |

Description: The kind of boundary prolongation for the stress-energy tensor
| ||

Range | Default: Lagrange | |

L̂agrange$ | standard prolongation (requires several time levels)
| |

n̂one$ | no prolongation (use this if you do not have enough time levels
active)
| |

any other supported prolongation type
| ||

stress_energy_storage | Scope: private | BOOLEAN |

Description: Should the stress-energy tensor have storage?
| ||

Default: no | ||

timelevels | Scope: private | INT |

Description: Number of time levels
| ||

Range | Default: 1 | |

0:3 | ||

stress_energy_at_rhs | Scope: restricted | BOOLEAN |

Description: Should the stress-energy tensor be calculated for the RHS evaluation?
| ||

Default: no | ||

support_old_calctmunu_mechanism | Scope: restricted | BOOLEAN |

Description: Should the old CalcTmunu.inc mechanism be supported? This is deprecated.
| ||

Default: no | ||

Implements:

tmunubase

Inherits:

admbase

staticconformal

Group Names | Variable Names | Details | |

stress_energy_state | stress_energy_state | compact | 0 |

description | State of storage for stress-energy tensor | ||

dimensions | 0 | ||

distribution | CONSTANT | ||

group type | SCALAR | ||

timelevels | 1 | ||

variable type | INT | ||

stress_energy_scalar | compact | 0 | |

eTtt | description | Stress-energy tensor | |

description | 3-scalar part T_00 | ||

dimensions | 3 | ||

distribution | DEFAULT | ||

group type | GF | ||

tags | tensortypealias=”Scalar” ProlongationParameter=”TmunuBase::prolongation_type” | ||

timelevels | 3 | ||

variable type | REAL | ||

stress_energy_vector | compact | 0 | |

eTtx | description | Stress-energy tensor | |

description | 3-vector part T_0i | ||

eTty | dimensions | 3 | |

eTtz | distribution | DEFAULT | |

group type | GF | ||

tags | tensortypealias=”D” ProlongationParameter=”TmunuBase::prolongation_type” | ||

timelevels | 3 | ||

variable type | REAL | ||

stress_energy_tensor | compact | 0 | |

eTxx | description | Stress-energy tensor | |

description | 3-tensor part T_ij | ||

eTxy | dimensions | 3 | |

eTxz | distribution | DEFAULT | |

eTyy | group type | GF | |

eTyz | tags | tensortypealias=”DD_sym” ProlongationParameter=”TmunuBase::prolongation_type” | |

eTzz | timelevels | 3 | |

variable type | REAL | ||

This section lists all the variables which are assigned storage by thorn EinsteinBase/TmunuBase. Storage can either last for the duration of the run (Always means that if this thorn is activated storage will be assigned, Conditional means that if this thorn is activated storage will be assigned for the duration of the run if some condition is met), or can be turned on for the duration of a schedule function.

Always: | Conditional: |

stress_energy_state | stress_energy_scalar[1] |

stress_energy_vector[1] | |

stress_energy_tensor[1] | |

stress_energy_scalar[2] | |

stress_energy_vector[2] | |

stress_energy_tensor[2] | |

stress_energy_scalar[3] | |

stress_energy_vector[3] | |

stress_energy_tensor[3] | |

CCTK_WRAGH

tmunubase_setstressenergystate

set the stress_energy_state variable

Before: | mol_register | |

Language: | fortran | |

Options: | global | |

Type: | function | |

Writes: | tmunubase::stress_energy_state(everywhere) | |

CCTK_PARAMCHECK

tmunubase_paramcheck

check that no deprecated parameters are used.

Language: | c | |

Options: | global | |

Type: | function | |

MoL_PostStep (conditional)

settmunu

group for calculating the stress-energy tensor

After: | admbase_setadmvars | |

Type: | group | |

SetTmunu (conditional)

tmunubase_zerotmunu

initialise the stress-energy tensor to zero

Language: | fortran | |

Type: | function | |

Writes: | tmunubase::stress_energy_scalar(everywhere) | |

tmunubase::stress_energy_vector(everywhere) | ||

tmunubase::stress_energy_tensor(everywhere) | ||

SetTmunu (conditional)

addtotmunu

add to the stress-energy tensor here

After: | tmunubase_settmunu | |

tmunubase_zerotmunu | ||

Type: | group | |