bssn – SPHINCS

type, public, extends(tpo) :: bssn

TYPE representing the $\mathrm{BSSNOK}$ formulation of the Einstein equations

Inherits

Variables

A_BSSN3_ll GC GC_int GC_l2 GC_loo GC_parts GC_parts_int GC_parts_l2 GC_parts_loo Gamma_u HC HC_int HC_l2 HC_loo HC_parts HC_parts_int HC_parts_l2 HC_parts_loo K_phys3_ll MC MC_int MC_l2 MC_loo MC_parts MC_parts_int MC_parts_l2 MC_parts_loo Ricci_ll Ricci_scalar S S_parts bssn_computer_timer call_flag cons_step coords export_bin export_constraints export_constraints_details export_constraints_x export_constraints_xy export_form_x export_form_xy g_BSSN3_ll g_phys3_ll grid_timer importer_timer lapse levels n_matter nlevels npoints_xaxis phi rad_coord rho rho_parts shift_u tpo_id_number trK

Type-Bound Procedures

abs_values_in analyze_constraint compute_adm_momentum_fluid_m2p compute_and_print_tpo_constraints compute_and_print_tpo_constraints_grid compute_and_print_tpo_constraints_particles compute_and_print_tpo_variables compute_ricci deallocate_fields deallocate_standard_tpo_variables define_allocate_fields destruct_bssn get_HC get_HC_parts get_MC get_MC_parts get_dx get_dy get_dz get_grid_point get_levels get_ngrid_x get_ngrid_y get_ngrid_z get_nlevels get_xR get_yR get_zR print_formatted_id_tpo_variables print_summary read_bssn_dump_print_formatted setup_standard_tpo_variables test_recovery_m2p

Source Code

bssn

Components

Type	Visibility	Attributes		Name		Initial
type(grid_function),	public		::	A_BSSN3_ll			Conformal traceless extrinsic curvature $A_{ij}$
type(grid_function),	public		::	GC			Connection constraint computed with the $\mathrm{ID}$ on the mesh
double precision,	public,	DIMENSION(:,:), ALLOCATABLE	::	GC_int			Integral of the connection constraint computed with the $\mathrm{ID}$ on the mesh
double precision,	public,	DIMENSION(:,:), ALLOCATABLE	::	GC_l2			$\ell_2$ norm of the connection constraint computed with the $\mathrm{ID}$ on the mesh
double precision,	public,	DIMENSION(:,:), ALLOCATABLE	::	GC_loo			$\ell_\infty$ norm, i.e., supremum of the absolute value, of the connection constraint computed with the $\mathrm{ID}$ on the mesh
type(grid_function),	public		::	GC_parts			Connection constraint computed with the $\mathrm{BSSNOK}$ $\mathrm{ID}$ on the mesh, and the hydrodynamical $\mathrm{ID}$ mapped from the particles to the mesh
double precision,	public,	DIMENSION(:,:), ALLOCATABLE	::	GC_parts_int			Integral of the connection constraint computed with the $\mathrm{BSSNOK}$ $\mathrm{ID}$ on the mesh, and the hydrodynamical $\mathrm{ID}$ mapped from the particles to the mesh with the $\mathrm{ID}$ on the mesh
double precision,	public,	DIMENSION(:,:), ALLOCATABLE	::	GC_parts_l2			$\ell_2$ norm of the connection constraint computed with the $\mathrm{BSSNOK}$ $\mathrm{ID}$ on the mesh, and the hydrodynamical $\mathrm{ID}$ mapped from the particles to the mesh
double precision,	public,	DIMENSION(:,:), ALLOCATABLE	::	GC_parts_loo			$\ell_\infty$ norm, i.e., supremum of the absolute value, of the connection constraint computed with the $\mathrm{BSSNOK}$ $\mathrm{ID}$ on the mesh, and the hydrodynamical $\mathrm{ID}$ mapped from the particles to the mesh
type(grid_function),	public		::	Gamma_u			Conformal connection $\bar{\Gamma} ^i_{jk}$
type(grid_function_scalar),	public		::	HC			Grid scalar function storing the Hamiltonian constraint (violations) computed using the ID on the mesh
double precision,	public,	DIMENSION(:), ALLOCATABLE	::	HC_int			Integral the Hamiltonian constraint computed using the stress-energy tensor mapped from the particles
double precision,	public,	DIMENSION(:), ALLOCATABLE	::	HC_l2			$\ell_2$ norm of the Hamiltonian constraint computed on the mesh
double precision,	public,	DIMENSION(:), ALLOCATABLE	::	HC_loo			$\ell_\infty$ norm of the Hamiltonian constraint computed on the mesh (i.e., its maximum)
type(grid_function_scalar),	public		::	HC_parts			Grid scalar function storing the Hamiltonian constraint (violations) computed using the stress-energy tensor mapped from the particles to the mesh
double precision,	public,	DIMENSION(:), ALLOCATABLE	::	HC_parts_int			Integral the Hamiltonian constraint computed on the mesh
double precision,	public,	DIMENSION(:), ALLOCATABLE	::	HC_parts_l2			$\ell_2$ norm of the Hamiltonian constraint computed on the mesh, using the stress-energy tensor mapped from the particles
double precision,	public,	DIMENSION(:), ALLOCATABLE	::	HC_parts_loo			$\ell_\infty$ norm of the Hamiltonian constraint computed on the mesh, using the stress-energy tensor mapped from the particles (i.e., its maximum)
type(grid_function),	public		::	K_phys3_ll			Grid function storing the extrinsic curvature
type(grid_function),	public		::	MC			Grid function storing the momentum constraint (violations) computed using the ID on the mesh
double precision,	public,	DIMENSION(:,:), ALLOCATABLE	::	MC_int			Integral of the momentum constraint computed on the mesh
double precision,	public,	DIMENSION(:,:), ALLOCATABLE	::	MC_l2			$\ell_2$ norm of the momentum constraint computed on the mesh
double precision,	public,	DIMENSION(:,:), ALLOCATABLE	::	MC_loo			$\ell_\infty$ norm of the momentum constraint computed on the mesh (i.e., its maximum)
type(grid_function),	public		::	MC_parts			Grid function storing the momentum constraint (violations) computed using the stress-energy tensor mapped from the particles to the mesh
double precision,	public,	DIMENSION(:,:), ALLOCATABLE	::	MC_parts_int			Integral of the momentum constraint computed using the stress-energy tensor mapped from the particles
double precision,	public,	DIMENSION(:,:), ALLOCATABLE	::	MC_parts_l2			$\ell_2$ norm of the Hamiltonian constraint computed on the mesh, using the stress-energy tensor mapped from the particles
double precision,	public,	DIMENSION(:,:), ALLOCATABLE	::	MC_parts_loo			$\ell_\infty$ norm of the momentum constraint computed on the mesh, using the stress-energy tensor mapped from the particles (i.e., its maximum)
type(grid_function),	public		::	Ricci_ll			Ricci tensor $R_{ij}$
type(grid_function_scalar),	public		::	Ricci_scalar			Ricci scalar $R^\mu{}_nu$
type(grid_function),	public		::	S			Grid function storing the matter source in the momentum constraint computed using the ID on the mesh, multiplied by $8\pi$
type(grid_function),	public		::	S_parts			Grid function storing the matter source in the momentum constraint computed using the stress-energy tensor mapped from the particles to the mesh, multiplied by $8\pi$
type(timer),	public		::	bssn_computer_timer			Timer that times how long it takes to compute the $\mathrm{BSSNOK}$ variables on the refined mesh
integer,	public		::	call_flag	=	0	Flag set to a value different than 0 if the SUBROUTINE compute_and_print_bssn_variables is called
integer,	public		::	cons_step			Constraint violations are printed to file every cons_step-th grid point
type(grid_function),	public		::	coords			Grid function storing the Cartesian coordinates
logical,	public		::	export_bin			`.TRUE.` if the binary files for SPHINCS_BSSN are to be exported, `.FALSE.` otherwise
logical,	public		::	export_constraints			`.TRUE.` if the constraint violations are to be printed to file, `.FALSE.` otherwise
logical,	public		::	export_constraints_details			`.TRUE.` if the points at which the constraints violations are within the intervals $[0,10^{-7}],[10^3,\infty],[10^n,10^m]$ , with $n\in\{-7,2\}$ and $m=n+1$ , are to be printed to file; `.FALSE.` otherwise
logical,	public		::	export_constraints_x			`.TRUE.` if only the constrain violations on the $x$ axis are to be
logical,	public		::	export_constraints_xy			`.TRUE.` if only the constrain violations on the $xy$ plane are to be
logical,	public		::	export_form_x			`.TRUE.` if the $\mathrm{ID}$ in the formatted files is to be on the x axis only, `.FALSE.` otherwise
logical,	public		::	export_form_xy			`.TRUE.` if the $\mathrm{ID}$ in the formatted files is to be on the xy plane only, `.FALSE.` otherwise
type(grid_function),	public		::	g_BSSN3_ll			Conformal spatial metric $\gamma_{ij}$
type(grid_function),	public		::	g_phys3_ll			Grid function storing the spatial metric
type(timer),	public		::	grid_timer			Timer that times how long it takes to set up the grid and allocate the grid functions
type(timer),	public		::	importer_timer			Timer that times how long it takes to import the $\texttt{LORENE}$ ID on the mesh
type(grid_function_scalar),	public		::	lapse			Grid scalar function storing the lapse function
type(level),	public,	DIMENSION(:), ALLOCATABLE	::	levels			Array containing the information on each refinement level
integer,	public		::	n_matter			Number of matter objects in the physical system
integer,	public		::	nlevels			Number of refinement levels
integer,	public,	DIMENSION(:), ALLOCATABLE	::	npoints_xaxis			Array containing the number of mesh points of the highest-resolution refinement level across the x-axis-size of the matter objects
type(grid_function_scalar),	public		::	phi			Conformal factor $\phi$
type(grid_function_scalar),	public		::	rad_coord			Grid scalar function storing the radial coordinates of each grid point
type(grid_function_scalar),	public		::	rho			Grid scalar function storing the matter source in the Hamiltonian constraint computed using the ID on the mesh, multiplied by $16\pi$
type(grid_function_scalar),	public		::	rho_parts			Grid scalar function storing the matter source in the Hamiltonian constraint computed using the stress-energy tensor mapped from the particles to the mesh, multiplied by $16\pi$
type(grid_function),	public		::	shift_u			Grid function storing the shift vector
integer,	public		::	tpo_id_number			Negative integer that identifies the tpo object
type(grid_function_scalar),	public		::	trK			Trace of extrinsic curvature $K$

Constructor

public interface bssn

public interface construct_bssn()

Arguments
None

Finalization Procedures

final :: destructor

Destructor; finalizes members from both TYPES tpo and bssn, by calling destruct_bssn

public interface destructor()

Arguments
None

Type-Bound Procedures

procedure, public :: abs_values_in

interface

public module subroutine abs_values_in(this, lower_bound, upper_bound, constraint, l, export, unit_analysis, cnt)

Arguments

Type	Intent	Attributes		Name
class(tpo),	intent(inout)		::	this
double precision,	intent(in)		::	lower_bound
double precision,	intent(in)		::	upper_bound
double precision,	intent(in),	DIMENSION(:,:,:)	::	constraint
integer,	intent(in)		::	l
logical,	intent(in)		::	export
integer,	intent(in)		::	unit_analysis
integer,	intent(out)		::	cnt

procedure, public, NON_OVERRIDABLE :: analyze_constraint

Analyze a constraint (or an arbitrary scalar grid function) by examining its values at the refined mesh. Computes the number of mesh points at which the scalar grid function has values lying within predefined (hard-coded) intervals

Todo

complete this documentation entries with more details

interface

public module subroutine analyze_constraint(this, l, constraint, name_constraint, unit_logfile, name_analysis, l2_norm, loo_norm, integral, source)

Arguments

Type	Intent	Optional	Attributes		Name
class(tpo),	intent(inout)			::	this
integer,	intent(in)			::	l
double precision,	intent(in),		DIMENSION(:,:,:)	::	constraint
character(len=*),	intent(in)			::	name_constraint
integer,	intent(in)			::	unit_logfile
character(len=*),	intent(in)			::	name_analysis
double precision,	intent(out)			::	l2_norm
double precision,	intent(out)			::	loo_norm
double precision,	intent(out)			::	integral
double precision,	intent(in),	optional,	DIMENSION(:,:,:)	::	source

procedure, public, NON_OVERRIDABLE :: compute_adm_momentum_fluid_m2p

Computes an estimate of the $\mathrm{ADM}$ linear momentum of the fluid using the $\mathrm{SPH}$ hydro fields, and the spacetime metric mapped from the mesh

Todo

add reference

interface

public module subroutine compute_adm_momentum_fluid_m2p(this, parts, adm_mom)

Computes an estimate of the $\mathrm{ADM}$ linear momentum of the fluid using the $\mathrm{SPH}$ hydro fields, and the spacetime metric mapped from the mesh

Todo

add reference

Arguments

Type	Intent	Attributes		Name
class(tpo),	intent(in)		::	this	tpo object which this PROCEDURE is a member of
class(particles),	intent(in)		::	parts	particles object used to map the metric from the mesh to the particles, and to call the recovery procedures
double precision,	intent(out),	DIMENSION(3)	::	adm_mom	ADM linear momentum of the fluid computed using the metric mapped with the mesh-to-particle mapping

generic, public :: compute_and_print_tpo_constraints => compute_and_print_tpo_constraints_grid, compute_and_print_tpo_constraints_particles

Overloaded PROCEDURE to compute the constraints using only the $\mathrm{ID}$ on the refined mesh, or the spacetime $\mathrm{ID}$ on the refined mesh and the hydrodynamical $\mathrm{ID}$ mapped from the particles to the refined mesh

public interface compute_and_print_bssn_constraints_grid()

Arguments
None
public interface compute_and_print_bssn_constraints_particles()

Arguments
None

procedure, public :: compute_and_print_tpo_constraints_grid => compute_and_print_bssn_constraints_grid

Computes the $\mathrm{BSSNOK}$ constraints using the full $\mathrm{ID}$ on the refined mesh, prints a summary with the statistics for the constraints. Optionally, prints the constraints to a formatted file to be read by $\texttt{gnuplot}$ , and analyze the constraints by calling analyze_constraint

interface

public module subroutine compute_and_print_bssn_constraints_grid(this, id, namefile, name_logfile, points)

Interface to compute_and_print_tpo_constraints_grid

Arguments

Type	Intent	Optional	Attributes		Name
class(bssn),	intent(inout),		TARGET	::	this	bssn object to which this PROCEDURE is bound
class(idbase),	intent(inout)			::	id	idbase object used to read the hydrodynamical $\mathrm{ID}$ to the mesh
character(len=*),	intent(inout)			::	namefile
character(len=*),	intent(inout)			::	name_logfile
double precision,	intent(in),	optional,	DIMENSION(:,:,:,:), TARGET	::	points

procedure, public :: compute_and_print_tpo_constraints_particles => compute_and_print_bssn_constraints_particles

Computes the $\mathrm{BSSNOK}$ constraints using the $\mathrm{BSSNOK}$ $\mathrm{ID}$ on the refined mesh and the hydrodynamical $\mathrm{ID}$ mapped from the particles to the mesh, prints a summary with the statistics for the constraints. Optionally, prints the constraints to a formatted file to be read by $\texttt{gnuplot}$ , and analyze the constraints by calling analyze_constraint

interface

public module subroutine compute_and_print_bssn_constraints_particles(this, parts_obj, namefile, name_logfile, points)

Interface to compute_and_print_tpo_constraints_particles

Arguments

Type	Intent	Optional	Attributes		Name
class(bssn),	intent(inout),		TARGET	::	this	bssn object to which this PROCEDURE is bound
class(particles),	intent(inout)			::	parts_obj	particles object used to map the hydrodynamical $\mathrm{ID}$ to the mesh
character(len=*),	intent(inout)			::	namefile
character(len=*),	intent(inout)			::	name_logfile
double precision,	intent(in),	optional,	DIMENSION(:,:,:,:), TARGET	::	points

procedure, public :: compute_and_print_tpo_variables => compute_and_print_bssn_variables

Computes the $\mathrm{BSSNOK}$ variables at the particle positions, and optionally prints them to a binary file to be read by $\texttt{SPHINCS_BSSN}$ and $\texttt{splash}$ , and to a formatted file to be read by $\texttt{gnuplot}$ , by calling print_formatted_id_tpo_variables

interface

public module subroutine compute_and_print_bssn_variables(this, namefile)

Interface to compute_and_print_tpo_variables

Arguments

Type	Intent	Optional	Attributes		Name
class(bssn),	intent(inout)			::	this	bssn object to which this PROCEDURE is bound
character(len=*),	intent(inout),	optional		::	namefile

procedure, public :: compute_ricci

Computes the Ricci tensor and the Ricci scalar on the mesh

interface

public module subroutine compute_ricci(this)

Computes the Ricci tensor and the Ricci scalar on the mesh

Arguments

Type	Intent	Optional	Attributes		Name
class(bssn),	intent(inout)			::	this	bssn object to which this PROCEDURE is bound

procedure, public :: deallocate_fields => deallocate_bssn_fields

Deallocates memory for the bssn member arrays

interface

public module subroutine deallocate_bssn_fields(this)

Interface to deallocate_fields

Arguments

Type	Intent	Optional	Attributes		Name
class(bssn),	intent(inout)			::	this	bssn object to which this PROCEDURE is bound

procedure, public, NON_OVERRIDABLE :: deallocate_standard_tpo_variables

Deallocates memory for the standard 3+1 fields

interface

public module subroutine deallocate_standard_tpo_variables(this)

Arguments

Type	Intent	Optional	Attributes		Name
class(tpo),	intent(inout)			::	this

procedure, public :: define_allocate_fields => allocate_bssn_fields

Allocates memory for the bssn member grid functions

interface

public module subroutine allocate_bssn_fields(this)

Interface to define_allocate_fields

Arguments

Type	Intent	Optional	Attributes		Name
class(bssn),	intent(inout)			::	this	bssn object to which this PROCEDURE is bound

procedure, public :: destruct_bssn

Destructor for the EXTENDED TYPE bssn, not ABSTRACT TYPE tpo

interface

public module subroutine destruct_bssn(this)

Interface to destruct_bssn

Arguments

Type	Intent	Optional	Attributes		Name
class(bssn),	intent(inout)			::	this	bssn object to which this PROCEDURE is bound

procedure, public :: get_HC

interface

public module function get_HC(this, i, j, k, l) result(HC_value)

Arguments

Type	Intent		Name
class(tpo),	intent(inout)	::	this
integer,	intent(in)	::	i
integer,	intent(in)	::	j
integer,	intent(in)	::	k
integer,	intent(in)	::	l

Return Value double precision

procedure, public :: get_HC_parts

interface

public module function get_HC_parts(this, i, j, k, l) result(HC_value)

Arguments

Type	Intent		Name
class(tpo),	intent(inout)	::	this
integer,	intent(in)	::	i
integer,	intent(in)	::	j
integer,	intent(in)	::	k
integer,	intent(in)	::	l

Return Value double precision

procedure, public :: get_MC

interface

public module function get_MC(this, i, j, k, l) result(MC_value)

Arguments

Type	Intent		Name
class(tpo),	intent(inout)	::	this
integer,	intent(in)	::	i
integer,	intent(in)	::	j
integer,	intent(in)	::	k
integer,	intent(in)	::	l

Return Value double precision, DIMENSION(3)

procedure, public :: get_MC_parts

interface

public module function get_MC_parts(this, i, j, k, l) result(MC_value)

Arguments

Type	Intent		Name
class(tpo),	intent(inout)	::	this
integer,	intent(in)	::	i
integer,	intent(in)	::	j
integer,	intent(in)	::	k
integer,	intent(in)	::	l

Return Value double precision, DIMENSION(3)

procedure, public :: get_dx

interface

public module function get_dx(this, l) result(dx)

Arguments

Type	Intent	Optional	Attributes		Name
class(tpo),	intent(inout)			::	this
integer,	intent(in)			::	l

Return Value double precision

procedure, public :: get_dy

interface

public module function get_dy(this, l) result(dy)

Arguments

Type	Intent	Optional	Attributes		Name
class(tpo),	intent(inout)			::	this
integer,	intent(in)			::	l

Return Value double precision

procedure, public :: get_dz

interface

public module function get_dz(this, l) result(dz)

Arguments

Type	Intent	Optional	Attributes		Name
class(tpo),	intent(inout)			::	this
integer,	intent(in)			::	l

Return Value double precision

procedure, public :: get_grid_point

interface

public module function get_grid_point(this, i, j, k, l) result(grid_point)

Arguments

Type	Intent		Name
class(tpo),	intent(inout)	::	this
integer,	intent(in)	::	i
integer,	intent(in)	::	j
integer,	intent(in)	::	k
integer,	intent(in)	::	l

Return Value double precision, DIMENSION(3)

procedure, public :: get_levels

interface

public module function get_levels(this) result(levels)

Arguments

Type	Intent	Optional	Attributes		Name
class(tpo),	intent(inout)			::	this

Return Value type(level), DIMENSION(:), ALLOCATABLE

procedure, public :: get_ngrid_x

interface

public module function get_ngrid_x(this, l) result(ngrid_x)

Arguments

Type	Intent	Optional	Attributes		Name
class(tpo),	intent(inout)			::	this
integer,	intent(in)			::	l

Return Value integer

procedure, public :: get_ngrid_y

interface

public module function get_ngrid_y(this, l) result(ngrid_y)

Arguments

Type	Intent	Optional	Attributes		Name
class(tpo),	intent(inout)			::	this
integer,	intent(in)			::	l

Return Value integer

procedure, public :: get_ngrid_z

interface

public module function get_ngrid_z(this, l) result(ngrid_z)

Arguments

Type	Intent	Optional	Attributes		Name
class(tpo),	intent(inout)			::	this
integer,	intent(in)			::	l

Return Value integer

procedure, public :: get_nlevels

interface

public module function get_nlevels(this) result(nlevels)

Arguments

Type	Intent	Optional	Attributes		Name
class(tpo),	intent(inout)			::	this

Return Value integer

procedure, public :: get_xR

interface

public module function get_xR(this, l) result(xR)

Arguments

Type	Intent	Optional	Attributes		Name
class(tpo),	intent(inout)			::	this
integer,	intent(in)			::	l

Return Value double precision

procedure, public :: get_yR

interface

public module function get_yR(this, l) result(yR)

Arguments

Type	Intent	Optional	Attributes		Name
class(tpo),	intent(inout)			::	this
integer,	intent(in)			::	l

Return Value double precision

procedure, public :: get_zR

interface

public module function get_zR(this, l) result(zR)

Arguments

Type	Intent	Optional	Attributes		Name
class(tpo),	intent(inout)			::	this
integer,	intent(in)			::	l

Return Value double precision

procedure, public :: print_formatted_id_tpo_variables => print_formatted_id_bssn_variables

Prints the $\mathrm{BSSNOK}$ $\mathrm{ID}$ to a formatted file

interface

public module subroutine print_formatted_id_bssn_variables(this, points, namefile)

Interface to print_formatted_id_tpo_variables

Arguments

Type	Intent	Optional	Attributes		Name
class(bssn),	intent(inout)			::	this	bssn object to which this PROCEDURE is bound
double precision,	intent(in),	optional,	DIMENSION(:,:,:,:)	::	points
character(len=*),	intent(inout),	optional		::	namefile

procedure, public, NON_OVERRIDABLE :: print_summary

Prints a summary about the features of the refined mesh

interface

public module subroutine print_summary(this)

Prints a summary of the properties of the refined mesh, and optionally, to a formatted file whose name is given as the optional argument filename

Arguments

Type	Intent	Optional	Attributes		Name
class(tpo),	intent(inout)			::	this	Name of the formatted file to print the summary to

procedure, public :: read_bssn_dump_print_formatted

Reads the binary $\mathrm{ID}$ file printed by compute_and_print_tpo_variables

interface

public module subroutine read_bssn_dump_print_formatted(this, namefile_bin, namefile)

Interface to read_bssn_dump_print_formatted

Arguments

Type	Intent	Optional		Name
class(bssn),	intent(inout)		::	this	bssn object to which this PROCEDURE is bound
character(len=*),	intent(inout),	optional	::	namefile_bin
character(len=*),	intent(inout),	optional	::	namefile

procedure, public, NON_OVERRIDABLE :: setup_standard_tpo_variables

Set up the refined mesh by reading the gravity_grid_parameter.dat parameter file, and read the standard 3+1 $\mathrm{ID}$ using the given idbase object, on the refined mesh

interface

public module subroutine setup_standard_tpo_variables(tpof, id, dx, dy, dz)

Arguments

Type	Intent	Optional		Name
class(tpo),	intent(inout)		::	tpof
class(idbase),	intent(inout)		::	id
double precision,	intent(in),	optional	::	dx
double precision,	intent(in),	optional	::	dy
double precision,	intent(in),	optional	::	dz

procedure, public, NON_OVERRIDABLE :: test_recovery_m2p

Computes the conserved variables from the physical ones, and vice versa, to test that the recovered physical variables are the same to those computed from the $\mathrm{ID}$. Uses the metric mapped from the grid to the particles.

Todo

add reference for recovery

interface

public module subroutine test_recovery_m2p(this, parts, namefile)

Tests the recovery. Computes the conserved variables from the physical ones, and then the physical ones from the conserved ones. It then compares the variables computed with the recovery PROCEDURES, with those computed with $\texttt{SPHINCS_ID}$. Uses the mesh-2-particle.

Todo

add reference for recovery

Arguments

Type	Intent		Name
class(tpo),	intent(in)	::	this	tpo object which this PROCEDURE is a member of
class(particles),	intent(in)	::	parts	particles object used to map the metric from the mesh to the particles, and to call the recovery procedures
character(len=*),	intent(inout)	::	namefile	Name of the formatted file where the data is printed

Source Code

  TYPE, EXTENDS(tpo):: bssn
  !# TYPE representing the |bssn| formulation of the |ee|


    INTEGER:: call_flag= 0
    !# Flag set to a value different than 0 if the SUBROUTINE
    !  compute_and_print_bssn_variables is called

    !
    !-- Arrays storing the BSSN variables for the |id| on the grid
    !

    TYPE(grid_function):: Gamma_u
    !! Conformal connection \(\bar{\Gamma} ^i_{jk}\)

    TYPE(grid_function_scalar):: phi
    !! Conformal factor \(\phi \)

    TYPE(grid_function_scalar):: trK
    !! Trace of extrinsic curvature \(K \)

    TYPE(grid_function):: A_BSSN3_ll
    !! Conformal traceless extrinsic curvature \(A_{ij} \)

    TYPE(grid_function):: g_BSSN3_ll
    !! Conformal spatial metric \(\gamma_{ij} \)

    TYPE(grid_function):: Ricci_ll
    !! Ricci tensor \(R_{ij} \)

    TYPE(grid_function_scalar):: Ricci_scalar
    !! Ricci scalar \(R^\mu{}_nu\)

    !
    !-- Connection constraints and its l2 norm and loo norm
    !

    TYPE(grid_function):: GC
    !! Connection constraint computed with the |id| on the mesh
    TYPE(grid_function):: GC_parts
    !# Connection constraint computed with the |bssn| |id| on the mesh, and
    !  the hydrodynamical |id| mapped from the particles to the mesh

    DOUBLE PRECISION, DIMENSION(:,:), ALLOCATABLE:: GC_l2
    !# \(\ell_2\) norm of the connection constraint computed
    !  with the |id| on the mesh
    DOUBLE PRECISION, DIMENSION(:,:), ALLOCATABLE:: GC_parts_l2
    !# \(\ell_2\) norm of the connection constraint computed with the |bssn|
    !  |id| on the mesh, and the hydrodynamical |id| mapped from the particles
    !  to the mesh
    DOUBLE PRECISION, DIMENSION(:,:), ALLOCATABLE:: GC_loo
    !# \(\ell_\infty\) norm, i.e., supremum of the absolute value, of the
    !  connection constraint computed with the |id| on the mesh
    DOUBLE PRECISION, DIMENSION(:,:), ALLOCATABLE:: GC_parts_loo
    !# \(\ell_\infty\) norm, i.e., supremum of the absolute value, of the
    !  connection constraint computed with the |bssn| |id| on the mesh,
    !  and the hydrodynamical |id| mapped from the particles to the mesh
    DOUBLE PRECISION, DIMENSION(:,:), ALLOCATABLE:: GC_int
    !# Integral of the connection constraint computed with the |id| on the mesh
    DOUBLE PRECISION, DIMENSION(:,:), ALLOCATABLE:: GC_parts_int
    !# Integral of the connection constraint computed with the |bssn| |id| on
    !  the mesh, and the hydrodynamical |id| mapped from the particles to the
    !  mesh with the |id| on the mesh

    LOGICAL, PUBLIC:: export_bin
    !# `.TRUE.` if the binary files for SPHINCS_BSSN are to be exported,
    !  `.FALSE.` otherwise
    LOGICAL, PUBLIC:: export_form_xy
    !# `.TRUE.` if the |id| in the formatted files is to be on the xy plane
    !  only, `.FALSE.` otherwise
    LOGICAL, PUBLIC:: export_form_x
    !# `.TRUE.` if the |id| in the formatted files is to be on the x axis
    !  only, `.FALSE.` otherwise

    TYPE(timer):: bssn_computer_timer
    !# Timer that times how long it takes to compute the |bssn| variables on
    !  the refined mesh


    CONTAINS


    !-------------------!
    !--  SUBROUTINES  --!
    !-------------------!


    PROCEDURE:: define_allocate_fields => allocate_bssn_fields
    !! Allocates memory for the [[bssn]] member grid functions

    PROCEDURE:: deallocate_fields => deallocate_bssn_fields
    !! Deallocates memory for the [[bssn]] member arrays

    PROCEDURE:: compute_and_print_tpo_variables &
                    => compute_and_print_bssn_variables
    !# Computes the |bssn| variables at the particle positions, and optionally
    !  prints them to a binary file to be read by \(\texttt{SPHINCS_BSSN}\)
    !  and \(\texttt{splash}\), and to a formatted file to be read by
    !  \(\texttt{gnuplot}\), by calling
    !  [[bssn:print_formatted_id_tpo_variables]]

    PROCEDURE:: print_formatted_id_tpo_variables &
                    => print_formatted_id_bssn_variables
    !! Prints the |bssn| |id| to a formatted file

    PROCEDURE:: compute_and_print_tpo_constraints_grid &
                    => compute_and_print_bssn_constraints_grid
    !# Computes the |bssn| constraints using the full |id| on the refined mesh,
    !  prints a summary with the statistics for the constraints. Optionally,
    !  prints the constraints to a formatted file to be read by
    !  \(\texttt{gnuplot}\), and analyze the constraints by calling
    !  [[tpo:analyze_constraint]]

    PROCEDURE:: compute_and_print_tpo_constraints_particles &
                    => compute_and_print_bssn_constraints_particles
    !# Computes the |bssn| constraints using the |bssn| |id| on the refined
    !  mesh and the hydrodynamical |id| mapped from the particles to the mesh,
    !  prints a summary with the statistics for the constraints. Optionally,
    !  prints the constraints to a formatted file to be read by
    !  \(\texttt{gnuplot}\), and analyze the constraints by calling
    !  [[tpo:analyze_constraint]]


    PROCEDURE:: destruct_bssn
    !# Destructor for the EXTENDED TYPE bssn, not ABSTRACT TYPE tpo

    FINAL    :: destructor
    !# Destructor; finalizes members from both TYPES tpo and bssn,
    !  by calling [[bssn:destruct_bssn]]

    PROCEDURE, PUBLIC:: read_bssn_dump_print_formatted
    !# Reads the binary |id| file printed by
    !  [[bssn:compute_and_print_tpo_variables]]

    PROCEDURE, PUBLIC:: compute_ricci
    !# Computes the Ricci tensor and the Ricci scalar on the mesh


  END TYPE bssn

bssn Derived Type

Contents

Source Code

type, public, extends(tpo) :: bssn

Inherits

Contents

Source Code

Components

Constructor

public interface bssn

public interface construct_bssn()

Arguments

Finalization Procedures

final :: destructor

public interface destructor()

Arguments

Type-Bound Procedures

procedure, public :: abs_values_in

interface

public module subroutine abs_values_in(this, lower_bound, upper_bound, constraint, l, export, unit_analysis, cnt) Implementation →

Arguments

procedure, public, NON_OVERRIDABLE :: analyze_constraint

Todo

interface

public module subroutine analyze_constraint(this, l, constraint, name_constraint, unit_logfile, name_analysis, l2_norm, loo_norm, integral, source) Implementation →

Arguments

procedure, public, NON_OVERRIDABLE :: compute_adm_momentum_fluid_m2p

Todo

interface

public module subroutine compute_adm_momentum_fluid_m2p(this, parts, adm_mom) Implementation →

Todo

Arguments

generic, public :: compute_and_print_tpo_constraints => compute_and_print_tpo_constraints_grid, compute_and_print_tpo_constraints_particles

public interface compute_and_print_bssn_constraints_grid()

Arguments

public interface compute_and_print_bssn_constraints_particles()

Arguments

procedure, public :: compute_and_print_tpo_constraints_grid => compute_and_print_bssn_constraints_grid

interface

public module subroutine compute_and_print_bssn_constraints_grid(this, id, namefile, name_logfile, points) Implementation →

Arguments

procedure, public :: compute_and_print_tpo_constraints_particles => compute_and_print_bssn_constraints_particles

interface

public module subroutine compute_and_print_bssn_constraints_particles(this, parts_obj, namefile, name_logfile, points) Implementation →

Arguments

procedure, public :: compute_and_print_tpo_variables => compute_and_print_bssn_variables

interface

public module subroutine compute_and_print_bssn_variables(this, namefile) Implementation →

Arguments

procedure, public :: compute_ricci

interface

public module subroutine compute_ricci(this) Implementation →

Arguments

procedure, public :: deallocate_fields => deallocate_bssn_fields

interface

public module subroutine deallocate_bssn_fields(this) Implementation →

Arguments

procedure, public, NON_OVERRIDABLE :: deallocate_standard_tpo_variables

interface

public module subroutine deallocate_standard_tpo_variables(this) Implementation →

Arguments

procedure, public :: define_allocate_fields => allocate_bssn_fields

interface

public module subroutine allocate_bssn_fields(this) Implementation →

Arguments

procedure, public :: destruct_bssn

interface

public module subroutine destruct_bssn(this) Implementation →

Arguments

procedure, public :: get_HC

interface

public module function get_HC(this, i, j, k, l) result(HC_value) Implementation →

Arguments

Return Value double precision

procedure, public :: get_HC_parts

interface

public module function get_HC_parts(this, i, j, k, l) result(HC_value) Implementation →

Arguments

Return Value double precision

procedure, public :: get_MC

public module subroutine abs_values_in(this, lower_bound, upper_bound, constraint, l, export, unit_analysis, cnt)

public module subroutine analyze_constraint(this, l, constraint, name_constraint, unit_logfile, name_analysis, l2_norm, loo_norm, integral, source)

public module subroutine compute_adm_momentum_fluid_m2p(this, parts, adm_mom)

public module subroutine compute_and_print_bssn_constraints_grid(this, id, namefile, name_logfile, points)

public module subroutine compute_and_print_bssn_constraints_particles(this, parts_obj, namefile, name_logfile, points)

public module subroutine compute_and_print_bssn_variables(this, namefile)

public module subroutine compute_ricci(this)

public module subroutine deallocate_bssn_fields(this)

public module subroutine deallocate_standard_tpo_variables(this)

public module subroutine allocate_bssn_fields(this)

public module subroutine destruct_bssn(this)

public module function get_HC(this, i, j, k, l) result(HC_value)

public module function get_HC_parts(this, i, j, k, l) result(HC_value)

public module function get_MC(this, i, j, k, l) result(MC_value)

public module function get_MC_parts(this, i, j, k, l) result(MC_value)

public module function get_dx(this, l) result(dx)

public module function get_dy(this, l) result(dy)

public module function get_dz(this, l) result(dz)

public module function get_grid_point(this, i, j, k, l) result(grid_point)

public module function get_levels(this) result(levels)

public module function get_ngrid_x(this, l) result(ngrid_x)

public module function get_ngrid_y(this, l) result(ngrid_y)

public module function get_ngrid_z(this, l) result(ngrid_z)

public module function get_nlevels(this) result(nlevels)

public module function get_xR(this, l) result(xR)