Utility routines for bubble model setup, coordinate transforms, array sampling, and special functions. More...

Functions/Subroutines
subroutine, public	s_comp_n_from_prim (vftmp, rtmp, ntmp, weights)
	Computes the bubble number density n from the primitive variables.
subroutine, public	s_comp_n_from_cons (vftmp, nrtmp, ntmp, weights)
	Compute the bubble number density from the conservative void fraction and weighted bubble radii.
impure subroutine, public	s_print_2d_array (a, div)
	Print a 2D real array to standard output, optionally dividing each element by a given scalar.
impure subroutine, public	s_initialize_bubbles_model ()
	Initialize bubble model arrays for Euler or Lagrangian bubbles with polytropic or non-polytropic gas.
impure subroutine	s_initialize_bubble_vars ()
	Set bubble physical parameters and nondimensional numbers from the input configuration.
impure subroutine, public	s_initialize_nonpoly ()
	Initializes non-polydisperse bubble modeling.
elemental subroutine, public	s_transcoeff (omega, peclet, re_trans, im_trans)
	Computes the transfer coefficient for the non-polytropic bubble compression process.
elemental subroutine, public	s_int_to_str (i, res)
	Convert an integer to its trimmed string representation.
subroutine, public	s_simpson (local_weight, local_r0)
	Computes the Simpson weights for quadrature.
pure real(wp) function, dimension(3), public	f_cross (a, b)
	Compute the cross product of two vectors.
elemental subroutine, public	s_swap (lhs, rhs)
	Swap two real numbers.
real(wp) function, dimension(1:4, 1:4), public	f_create_transform_matrix (param, center)
	Create a transformation matrix.
subroutine, public	s_transform_vec (vec, matrix)
	Transform a vector by a matrix.
subroutine, public	s_transform_triangle (triangle, matrix, matrix_n)
	Transform a triangle by a matrix, one vertex at a time.
subroutine, public	s_transform_model (model, matrix, matrix_n)
	Transform a model by a matrix, one triangle at a time.
type(t_bbox) function, public	f_create_bbox (model)
	Create a bounding box for a model.
elemental logical function, public	f_xor (lhs, rhs)
	Perform XOR on lhs and rhs.
elemental integer function, public	f_logical_to_int (predicate)
	Convert a logical to 1 or 0.
real(wp) function, public	real_ylm (theta, phi, l, m)
	Real spherical harmonic Y_lm(theta, phi). theta = polar angle from +z (acos(z/r)), phi = atan2(y,x). Uses associated Legendre P_l^\|m\|(cos theta). Standard normalisation.
recursive real(wp) function, public	associated_legendre (x, l, m_order)
	Associated Legendre polynomial P_l^m(x) (Ferrers function, Condon-Shortley phase). Valid for integer l >= 0, 0 <= m <= l, and x in [-1,1]. Returns 0 for \|m\| > l or l < 0. Formulas: DLMF 14.10.3 (recurrence in degree), Wikipedia "Associated Legendre polynomials" (P_l^l and P_l^{l-1} identities). Recurrence: (l-m)P_l^m = (2l-1)x P_{l-1}^m - (l+m-1)P_{l-2}^m.
elemental integer(kind=int64_kind) function, public	double_factorial (n_in)
	Calculate the double factorial of an integer.
elemental integer(kind=int64_kind) function, public	factorial (n_in)
	Calculate the factorial of an integer.
real(wp) function, public	f_cut_on (x, eps)
	Calculate a smooth cut-on function that is zero for x values smaller than zero and goes to one, for generating smooth initial conditions.
real(wp) function, public	f_cut_off (x, eps)
	Calculate a smooth cut-off function that is one for x values smaller than zero and goes to zero, for generating smooth initial conditions.
real(wp) function	f_gx (x)
	Helper function for f_cut_on and f_cut_off.
subroutine, public	s_downsample_data (q_cons_vf, q_cons_temp, m_ds, n_ds, p_ds, m_glb_ds, n_glb_ds, p_glb_ds)
	Downsample conservative variable fields by a factor of 3 in each direction using volume averaging.
subroutine, public	s_upsample_data (q_cons_vf, q_cons_temp)
	Upsample conservative variable fields from a coarsened grid back to the original resolution using interpolation.

Detailed Description

Utility routines for bubble model setup, coordinate transforms, array sampling, and special functions.

Function/Subroutine Documentation

◆ associated_legendre()

recursive real(wp) function, public m_helper::associated_legendre	(	real(wp), intent(in)	x,
		integer, intent(in)	l,
		integer, intent(in)	m_order )

Associated Legendre polynomial P_l^m(x) (Ferrers function, Condon-Shortley phase). Valid for integer l >= 0, 0 <= m <= l, and x in [-1,1]. Returns 0 for |m| > l or l < 0. Formulas: DLMF 14.10.3 (recurrence in degree), Wikipedia "Associated Legendre polynomials" (P_l^l and P_l^{l-1} identities). Recurrence: (l-m)P_l^m = (2l-1)x P_{l-1}^m - (l+m-1)P_{l-2}^m.

Parameters

x	argument (typically cos(theta)), should be in [-1,1]
l	degree (>= 0)
m_order	order (0 <= m_order <= l)

Definition at line 978 of file m_helper.fpp.f90.

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◆ double_factorial()

elemental integer(kind=int64_kind) function, public m_helper::double_factorial ( integer, intent(in) n_in )

Calculate the double factorial of an integer.

Definition at line 1013 of file m_helper.fpp.f90.

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◆ f_create_bbox()

type(t_bbox) function, public m_helper::f_create_bbox ( type(t_model), intent(in) model )

Create a bounding box for a model.

Definition at line 898 of file m_helper.fpp.f90.

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◆ f_create_transform_matrix()

real(wp) function, dimension(1:4,1:4), public m_helper::f_create_transform_matrix	(	type(ic_model_parameters), intent(in)	param,
		real(wp), dimension(1:3), intent(in), optional	center )

Create a transformation matrix.

Definition at line 820 of file m_helper.fpp.f90.

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◆ f_cross()

pure real(wp) function, dimension(3), public m_helper::f_cross	(	real(wp), dimension(3), intent(in)	a,
		real(wp), dimension(3), intent(in)	b )

Compute the cross product of two vectors.

Definition at line 780 of file m_helper.fpp.f90.

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◆ f_cut_off()

real(wp) function, public m_helper::f_cut_off	(	real(wp), intent(in)	x,
		real(wp), intent(in)	eps )

Calculate a smooth cut-off function that is one for x values smaller than zero and goes to zero, for generating smooth initial conditions.

Definition at line 1049 of file m_helper.fpp.f90.

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◆ f_cut_on()

real(wp) function, public m_helper::f_cut_on	(	real(wp), intent(in)	x,
		real(wp), intent(in)	eps )

Calculate a smooth cut-on function that is zero for x values smaller than zero and goes to one, for generating smooth initial conditions.

Definition at line 1038 of file m_helper.fpp.f90.

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◆ f_gx()

real(wp) function m_helper::f_gx ( real(wp), intent(in) x )

private

Helper function for f_cut_on and f_cut_off.

Definition at line 1059 of file m_helper.fpp.f90.

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◆ f_logical_to_int()

elemental integer function, public m_helper::f_logical_to_int ( logical, intent(in) predicate )

Convert a logical to 1 or 0.

Definition at line 933 of file m_helper.fpp.f90.

◆ f_xor()

elemental logical function, public m_helper::f_xor	(	logical, intent(in)	lhs,
		logical, intent(in)	rhs )

Perform XOR on lhs and rhs.

Definition at line 923 of file m_helper.fpp.f90.

◆ factorial()

elemental integer(kind=int64_kind) function, public m_helper::factorial ( integer, intent(in) n_in )

Calculate the factorial of an integer.

Definition at line 1025 of file m_helper.fpp.f90.

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◆ real_ylm()

real(wp) function, public m_helper::real_ylm	(	real(wp), intent(in)	theta,
		real(wp), intent(in)	phi,
		integer, intent(in)	l,
		integer, intent(in)	m )

Real spherical harmonic Y_lm(theta, phi). theta = polar angle from +z (acos(z/r)), phi = atan2(y,x). Uses associated Legendre P_l^|m|(cos theta). Standard normalisation.

Definition at line 948 of file m_helper.fpp.f90.

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◆ s_comp_n_from_cons()

subroutine, public m_helper::s_comp_n_from_cons	(	real(wp), intent(in)	vftmp,
		real(wp), dimension(nb), intent(in)	nrtmp,
		real(wp), intent(out)	ntmp,
		real(wp), dimension(nb), intent(in)	weights )

Compute the bubble number density from the conservative void fraction and weighted bubble radii.

Definition at line 374 of file m_helper.fpp.f90.

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◆ s_comp_n_from_prim()

subroutine, public m_helper::s_comp_n_from_prim	(	real(wp), intent(in)	vftmp,
		real(wp), dimension(nb), intent(in)	rtmp,
		real(wp), intent(out)	ntmp,
		real(wp), dimension(nb), intent(in)	weights )

Computes the bubble number density n from the primitive variables.

Definition at line 345 of file m_helper.fpp.f90.

◆ s_downsample_data()

subroutine, public m_helper::s_downsample_data	(	type(scalar_field), dimension(sys_size), intent(inout)	q_cons_vf,
		type(scalar_field), dimension(sys_size), intent(inout)	q_cons_temp,
		integer, intent(inout)	m_ds,
		integer, intent(inout)	n_ds,
		integer, intent(inout)	p_ds,
		integer, intent(inout)	m_glb_ds,
		integer, intent(inout)	n_glb_ds,
		integer, intent(inout)	p_glb_ds )

Downsample conservative variable fields by a factor of 3 in each direction using volume averaging.

Definition at line 1073 of file m_helper.fpp.f90.

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◆ s_initialize_bubble_vars()

impure subroutine m_helper::s_initialize_bubble_vars

private

Set bubble physical parameters and nondimensional numbers from the input configuration.

Definition at line 609 of file m_helper.fpp.f90.

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◆ s_initialize_bubbles_model()

impure subroutine, public m_helper::s_initialize_bubbles_model

Initialize bubble model arrays for Euler or Lagrangian bubbles with polytropic or non-polytropic gas.

Definition at line 433 of file m_helper.fpp.f90.

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◆ s_initialize_nonpoly()

impure subroutine, public m_helper::s_initialize_nonpoly

Initializes non-polydisperse bubble modeling.

Definition at line 662 of file m_helper.fpp.f90.

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◆ s_int_to_str()

elemental subroutine, public m_helper::s_int_to_str	(	integer, intent(in)	i,
		character(len=*), intent(inout)	res )

Convert an integer to its trimmed string representation.

Definition at line 729 of file m_helper.fpp.f90.

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◆ s_print_2d_array()

impure subroutine, public m_helper::s_print_2d_array	(	real(wp), dimension(:,:), intent(in)	a,
		real(wp), intent(in), optional	div )

Print a 2D real array to standard output, optionally dividing each element by a given scalar.

Definition at line 403 of file m_helper.fpp.f90.

◆ s_simpson()

subroutine, public m_helper::s_simpson	(	real(wp), dimension(:), intent(inout)	local_weight,
		real(wp), dimension(:), intent(inout)	local_r0 )

Computes the Simpson weights for quadrature.

Definition at line 740 of file m_helper.fpp.f90.

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◆ s_swap()

elemental subroutine, public m_helper::s_swap	(	real(wp), intent(inout)	lhs,
		real(wp), intent(inout)	rhs )

Swap two real numbers.

Definition at line 808 of file m_helper.fpp.f90.

◆ s_transcoeff()

elemental subroutine, public m_helper::s_transcoeff	(	real(wp), intent(in)	omega,
		real(wp), intent(in)	peclet,
		real(wp), intent(out)	re_trans,
		real(wp), intent(out)	im_trans )

Computes the transfer coefficient for the non-polytropic bubble compression process.

Definition at line 710 of file m_helper.fpp.f90.

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◆ s_transform_model()

subroutine, public m_helper::s_transform_model	(	type(t_model), intent(inout)	model,
		real(wp), dimension(1:4,1:4), intent(in)	matrix,
		real(wp), dimension(1:4,1:4), intent(in)	matrix_n )

Transform a model by a matrix, one triangle at a time.

Definition at line 885 of file m_helper.fpp.f90.

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◆ s_transform_triangle()

subroutine, public m_helper::s_transform_triangle	(	type(t_triangle), intent(inout)	triangle,
		real(wp), dimension(1:4,1:4), intent(in)	matrix,
		real(wp), dimension(1:4,1:4), intent(in)	matrix_n )

Transform a triangle by a matrix, one vertex at a time.

Definition at line 870 of file m_helper.fpp.f90.

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◆ s_transform_vec()

subroutine, public m_helper::s_transform_vec	(	real(wp), dimension(1:3), intent(inout)	vec,
		real(wp), dimension(1:4,1:4), intent(in)	matrix )

Transform a vector by a matrix.

Definition at line 858 of file m_helper.fpp.f90.

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◆ s_upsample_data()

subroutine, public m_helper::s_upsample_data	(	type(scalar_field), dimension(sys_size), intent(inout)	q_cons_vf,
		type(scalar_field), dimension(sys_size), intent(inout)	q_cons_temp )

Upsample conservative variable fields from a coarsened grid back to the original resolution using interpolation.

Definition at line 1115 of file m_helper.fpp.f90.

Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ associated_legendre()

◆ double_factorial()

◆ f_create_bbox()

◆ f_create_transform_matrix()

◆ f_cross()

◆ f_cut_off()

◆ f_cut_on()

◆ f_gx()

◆ f_logical_to_int()

◆ f_xor()

◆ factorial()

◆ real_ylm()

◆ s_comp_n_from_cons()

◆ s_comp_n_from_prim()

◆ s_downsample_data()

◆ s_initialize_bubble_vars()

◆ s_initialize_bubbles_model()

◆ s_initialize_nonpoly()

◆ s_int_to_str()

◆ s_print_2d_array()

◆ s_simpson()

◆ s_swap()

◆ s_transcoeff()

◆ s_transform_model()

◆ s_transform_triangle()

◆ s_transform_vec()

◆ s_upsample_data()