Operators.

Functions/Subroutines
subroutine, public	dudxyz (du, u, dr, ds, dt, coef)
	Compute derivative of a scalar field along a single direction.

subroutine, public	div (res, ux, uy, uz, coef)
	Compute the divergence of a vector field.

subroutine, public	grad (ux, uy, uz, u, coef)
	Compute the gradient of a scalar field.

subroutine, public	opgrad (ux, uy, uz, u, coef, es, ee)
	Compute the weak gradient of a scalar field, i.e. the gradient multiplied by the mass matrix.

subroutine, public	ortho (x, glb_n_points, n)
	Othogonalize with regard to vector (1,1,1,1,1,1...,1)^T.

subroutine, public	cdtp (dtx, x, dr, ds, dt, coef, es, ee)
	Apply D^T to a scalar field, where D is the derivative matrix.

subroutine, public	conv1 (du, u, vx, vy, vz, xh, coef, es, ee)
	Compute the advection term.

subroutine	convect_scalar (du, u, c, xh_gll, xh_gl, coef_gll, coef_gl, gll_to_gl)
	Apply the convecting velocity c to the to the scalar field u, used in the OIFS scheme.

subroutine, public	curl (w1, w2, w3, u1, u2, u3, work1, work2, coef)

real(kind=rp) function, public	cfl (dt, u, v, w, xh, coef, nelv, gdim)

subroutine, public	strain_rate (s11, s22, s33, s12, s13, s23, u, v, w, coef)
	Compute the strain rate tensor, i.e 0.5 * du_i/dx_j + du_j/dx_i.

subroutine, public	lambda2op (lambda2, u, v, w, coef)
	Compute the Lambda2 field for a given velocity field.

subroutine, public	set_convect_rst (cr, cs, ct, cx, cy, cz, xh, coef)
	Transforms the convecting velocity field to the rst form of the GL space.

subroutine, public	runge_kutta (phi, c_r1, c_r23, c_r4, xh_gll, xh_gl, coef, coef_gl, gll_to_gl, tau, dtau, n, nel, n_gl)
	Compute one step of Runge Kutta time interpolation for OIFS scheme.

Function/Subroutine Documentation

◆ cdtp()

subroutine, public operators::cdtp	(	real(kind=rp), dimension(coef%xh%lxyz, coef%msh%nelv), intent(inout)	dtx,
		real(kind=rp), dimension(coef%xh%lxyz, coef%msh%nelv), intent(inout)	x,
		real(kind=rp), dimension(coef%xh%lxyz, coef%msh%nelv), intent(in)	dr,
		real(kind=rp), dimension(coef%xh%lxyz, coef%msh%nelv), intent(in)	ds,
		real(kind=rp), dimension(coef%xh%lxyz, coef%msh%nelv), intent(in)	dt,
		type(coef_t), intent(in)	coef,
		integer, optional	es,
		integer, optional	ee
	)

Parameters

dtx	Will store the result.
x	The values of the field.
dr	The derivative of r with respect to the chosen direction.
ds	The derivative of s with respect to the chosen direction.
dt	The derivative of t with respect to the chosen direction.
coef	The SEM coefficients.
es	Starting element index, optional, defaults to 1.
ee	Ending element index, optional, defaults to `nelv`.

Note: This needs to be revised... the loop over n1,n2 is probably unesccssary

Definition at line 235 of file operators.f90.

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◆ cfl()

real(kind=rp) function, public operators::cfl	(	real(kind=rp), intent(in)	dt,
		real(kind=rp), dimension(xh%lx, xh%ly, xh%lz, nelv), intent(in)	u,
		real(kind=rp), dimension(xh%lx, xh%ly, xh%lz, nelv), intent(in)	v,
		real(kind=rp), dimension(xh%lx, xh%ly, xh%lz, nelv), intent(in)	w,
		type(space_t), intent(in)	xh,
		type(coef_t), intent(in)	coef,
		integer, intent(in)	nelv,
		integer, intent(in)	gdim
	)

Definition at line 399 of file operators.f90.

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◆ conv1()

subroutine, public operators::conv1	(	real(kind=rp), dimension(xh%lxyz, coef%msh%nelv), intent(inout)	du,
		real(kind=rp), dimension(xh%lx, xh%ly, xh%lz, coef%msh%nelv), intent(inout)	u,
		real(kind=rp), dimension(xh%lx, xh%ly, xh%lz, coef%msh%nelv), intent(inout)	vx,
		real(kind=rp), dimension(xh%lx, xh%ly, xh%lz, coef%msh%nelv), intent(inout)	vy,
		real(kind=rp), dimension(xh%lx, xh%ly, xh%lz, coef%msh%nelv), intent(inout)	vz,
		type(space_t), intent(in)	xh,
		type(coef_t), intent(in)	coef,
		integer, optional	es,
		integer, optional	ee
	)

Parameters

du	Holds the result.
u	The advected field.
vx	The x component of the advecting velocity.
vy	The y component of the advecting velocity.
vz	The z component of the advecting velocity.
Xh	The function space for the fields involved.
coef	The SEM coefficients.
es	Starting element index, defaults to 1.
ee	Last element index, defaults to mesh size.

Definition at line 279 of file operators.f90.

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◆ convect_scalar()

subroutine operators::convect_scalar	(	real(kind=rp), dimension(xh_gll%lx, xh_gll%ly, xh_gll%lz, coef_gl%msh%nelv), intent(inout)	du,
		real(kind=rp), dimension(xh_gl%lx, xh_gl%lx, xh_gl%lx, coef_gl%msh%nelv), intent(inout)	u,
		real(kind=rp), dimension(xh_gl%lxyz, coef_gl%msh%nelv, 3), intent(inout)	c,
		type(space_t), intent(in)	xh_gll,
		type(space_t), intent(in)	xh_gl,
		type(coef_t), intent(in)	coef_gll,
		type(coef_t), intent(in)	coef_gl,
		type(interpolator_t), intent(inout)	gll_to_gl
	)

private

Parameters

du	Holds the result
c	The convecting velocity
u	The convected scalar field
Xh_GLL	The GLL space used in simulation
Xh_GL	The GL space used for dealiasing
coef	The coefficients of the original space in simulation
coef_GL	The coefficients of the GL space used for dealiasing
GLL_to_GL	the interpolator between the GLL and GL spaces

Note: This subroutine is equal to the convop_fst_3d of the NEK5000.; This subroutine is used specifically in the OIFS scheme, calculateing eq(17) in https://publications.anl.gov/anlpubs/2017/12/140626.pdf. The convecting term is calculated in the rst format and the GL grid. Then converted back to the GLL grid, going through an ADD gatter scatter operation at the element boundaries, before being multiplied by inverse of mass matrix.

Definition at line 331 of file operators.f90.

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◆ curl()

subroutine, public operators::curl	(	type(field_t), intent(inout)	w1,
		type(field_t), intent(inout)	w2,
		type(field_t), intent(inout)	w3,
		type(field_t), intent(in)	u1,
		type(field_t), intent(in)	u2,
		type(field_t), intent(in)	u3,
		type(field_t), intent(inout)	work1,
		type(field_t), intent(inout)	work2,
		type(coef_t), intent(in)	coef
	)

Definition at line 367 of file operators.f90.

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◆ div()

subroutine, public operators::div	(	real(kind=rp), dimension(coef%xh%lx, coef%xh%ly, coef%xh%lz, coef%msh%nelv), intent(inout)	res,
		real(kind=rp), dimension(coef%xh%lx, coef%xh%ly, coef%xh%lz, coef%msh%nelv), intent(in)	ux,
		real(kind=rp), dimension(coef%xh%lx, coef%xh%ly, coef%xh%lz, coef%msh%nelv), intent(in)	uy,
		real(kind=rp), dimension(coef%xh%lx, coef%xh%ly, coef%xh%lz, coef%msh%nelv), intent(in)	uz,
		type(coef_t), intent(in), target	coef
	)

Parameters

res	Holds the resulting divergence values.
ux	The x component of the vector field.
uy	The y component of the vector field.
uz	The z component of the vector field.
coef	The SEM coefficients.

Definition at line 100 of file operators.f90.

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◆ dudxyz()

subroutine, public operators::dudxyz	(	real(kind=rp), dimension(coef%xh%lx, coef%xh%ly, coef%xh%lz, coef%msh%nelv), intent(inout)	du,
		real(kind=rp), dimension(coef%xh%lx, coef%xh%ly, coef%xh%lz, coef%msh%nelv), intent(in)	u,
		real(kind=rp), dimension(coef%xh%lx, coef%xh%ly, coef%xh%lz, coef%msh%nelv), intent(in)	dr,
		real(kind=rp), dimension(coef%xh%lx, coef%xh%ly, coef%xh%lz, coef%msh%nelv), intent(in)	ds,
		real(kind=rp), dimension(coef%xh%lx, coef%xh%ly, coef%xh%lz, coef%msh%nelv), intent(in)	dt,
		type(coef_t), intent(in), target	coef
	)

Parameters

du	Holds the resulting derivative values.
u	The values of the field.
dr	The derivative of r with respect to the chosen direction.
ds	The derivative of s with respect to the chosen direction.
dt	The derivative of t with respect to the chosen direction.
coef	The SEM coefficients.

Definition at line 75 of file operators.f90.

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◆ grad()

subroutine, public operators::grad	(	real(kind=rp), dimension(coef%xh%lxyz, coef%msh%nelv), intent(inout)	ux,
		real(kind=rp), dimension(coef%xh%lxyz, coef%msh%nelv), intent(inout)	uy,
		real(kind=rp), dimension(coef%xh%lxyz, coef%msh%nelv), intent(inout)	uz,
		real(kind=rp), dimension(coef%xh%lxyz, coef%msh%nelv), intent(in)	u,
		type(coef_t), intent(in)	coef
	)

Parameters

ux	Will store the x component of the gradient.
uy	Will store the y component of the gradient.
uz	Will store the z component of the gradient.
u	The values of the field.
coef	The SEM coefficients.

Definition at line 145 of file operators.f90.

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◆ lambda2op()

subroutine, public operators::lambda2op	(	type(field_t), intent(inout)	lambda2,
		type(field_t), intent(in)	u,
		type(field_t), intent(in)	v,
		type(field_t), intent(in)	w,
		type(coef_t), intent(in)	coef
	)

Parameters

lambda2	Holds the computed Lambda2 field.
u	The x-velocity.
v	The y-velocity.
w	the z-velocity.
coef	The SEM coefficients.

Definition at line 508 of file operators.f90.

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◆ opgrad()

subroutine, public operators::opgrad	(	real(kind=rp), dimension(coef%xh%lxyz, coef%msh%nelv), intent(inout)	ux,
		real(kind=rp), dimension(coef%xh%lxyz, coef%msh%nelv), intent(inout)	uy,
		real(kind=rp), dimension(coef%xh%lxyz, coef%msh%nelv), intent(inout)	uz,
		real(kind=rp), dimension(coef%xh%lxyz, coef%msh%nelv), intent(in)	u,
		type(coef_t), intent(in)	coef,
		integer, optional	es,
		integer, optional	ee
	)

By providing es and ee, it is possible to compute only for a range of element indices.

Parameters

ux	Will store the x component of the gradient.
uy	Will store the y component of the gradient.
uz	Will store the z component of the gradient.
u	The values of the field.
coef	The SEM coefficients.
es	Starting element index, optional, defaults to 1.
ee	Ending element index, optional, defaults to `nelv`.

Note: Equals wgradm1 in Nek5000, the weak form of the gradient.

Definition at line 170 of file operators.f90.

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◆ ortho()

subroutine, public operators::ortho	(	real(kind=rp), dimension(n), intent(inout)	x,
		integer(kind=i8), intent(in)	glb_n_points,
		integer, intent(in)	n
	)

Parameters

x	The vector to orthogonolize.
glb_n_points	The global number of non-unique gll points in the grid.

Note: This is equivalent to subtracting the mean of x from each of its elements.

Definition at line 207 of file operators.f90.

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◆ runge_kutta()

subroutine, public operators::runge_kutta	(	real(kind=rp), dimension(n), intent(inout)	phi,
		real(kind=rp), dimension(3 * n_gl), intent(inout)	c_r1,
		real(kind=rp), dimension(3 * n_gl), intent(inout)	c_r23,
		real(kind=rp), dimension(3 * n_gl), intent(inout)	c_r4,
		type(space_t), intent(in)	xh_gll,
		type(space_t), intent(inout)	xh_gl,
		type(coef_t), intent(in)	coef,
		type(coef_t), intent(inout)	coef_gl,
		type(interpolator_t)	gll_to_gl,
		real(kind=rp), intent(inout)	tau,
		real(kind=rp), intent(inout)	dtau,
		integer, intent(in)	n,
		integer, intent(in)	nel,
		integer, intent(in)	n_gl
	)

Parameters

phi	The iterpolated field
c_r1	The covecting velocity for the first stage
c_r23	The convecting velocity for the second and third stage
c_r4	The convecting velocity for the fourth stage
Xh_GLL	The GLL space used in simulation
Xh_GL	The GL space used for dealiasing
coef	The coefficients of the original space in simulation
coef_GL	The coefficients of the GL space used for dealiasing
GLL_to_GL	the interpolator between the GLL and GL spaces
tau	The the starting time
dtau	The time step used for the Runge Kutta scheme
n	size of phi
nel	Total number of elements
n_GL	the size in the GL space

Definition at line 566 of file operators.f90.

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◆ set_convect_rst()

subroutine, public operators::set_convect_rst	(	real(kind=rp), dimension(xh%lxyz, coef%msh%nelv), intent(inout)	cr,
		real(kind=rp), dimension(xh%lxyz, coef%msh%nelv), intent(inout)	cs,
		real(kind=rp), dimension(xh%lxyz, coef%msh%nelv), intent(inout)	ct,
		real(kind=rp), dimension(xh%lxyz, coef%msh%nelv), intent(in)	cx,
		real(kind=rp), dimension(xh%lxyz, coef%msh%nelv), intent(in)	cy,
		real(kind=rp), dimension(xh%lxyz, coef%msh%nelv), intent(in)	cz,
		type(space_t), intent(inout)	xh,
		type(coef_t), intent(inout)	coef
	)

Parameters

cr	convecting velocity in r-direction
cs	convecting velocity in s-direction
ct	convecting velocity in t-direction
cx	convecting velocity in x-direction
cy	convecting velocity in y-direction
cz	convecting velocity in z-direction
Xh	The GL space used for dealiasing
coef	The coeffiecients of the GL space used for dealiasing

Note: This subroutine is equal to the set_convect_new subroutine of NEK5000

Definition at line 533 of file operators.f90.

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◆ strain_rate()

subroutine, public operators::strain_rate	(	real(kind=rp), dimension(u%xh%lx, u%xh%ly, u%xh%lz, u%msh%nelv), intent(inout)	s11,
		real(kind=rp), dimension(u%xh%lx, u%xh%ly, u%xh%lz, u%msh%nelv), intent(inout)	s22,
		real(kind=rp), dimension(u%xh%lx, u%xh%ly, u%xh%lz, u%msh%nelv), intent(inout)	s33,
		real(kind=rp), dimension(u%xh%lx, u%xh%ly, u%xh%lz, u%msh%nelv), intent(inout)	s12,
		real(kind=rp), dimension(u%xh%lx, u%xh%ly, u%xh%lz, u%msh%nelv), intent(inout)	s13,
		real(kind=rp), dimension(u%xh%lx, u%xh%ly, u%xh%lz, u%msh%nelv), intent(inout)	s23,
		type(field_t), intent(in)	u,
		type(field_t), intent(in)	v,
		type(field_t), intent(in)	w,
		type(coef_t), intent(in)	coef
	)

Parameters

s11	Will hold the 1,1 component of the strain rate tensor.
s22	Will hold the 2,2 component of the strain rate tensor.
s33	Will hold the 3,3 component of the strain rate tensor.
s12	Will hold the 1,2 component of the strain rate tensor.
s13	Will hold the 1,3 component of the strain rate tensor.
s23	Will hold the 2,3 component of the strain rate tensor.
u	The x component of velocity.
v	The y component of velocity.
w	The z component of velocity.
coef	The SEM coefficients.

Note: Similar to comp_sij in Nek5000.

Parameters

[in] w velocity components

Definition at line 435 of file operators.f90.

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Functions/Subroutines

Function/Subroutine Documentation

◆ cdtp()

◆ cfl()

◆ conv1()

◆ convect_scalar()

◆ curl()

◆ div()

◆ dudxyz()

◆ grad()

◆ lambda2op()

◆ opgrad()

◆ ortho()

◆ runge_kutta()

◆ set_convect_rst()

◆ strain_rate()