adam_prism_leapfrog_pic_object

ADAM, leapfrog class definition.

Considering the following ODE system:

$$U_t=R(t,U)$$

where (U_t = \frac{dU}{dt}), U is the vector of state variables being a function of the time-like independent variable t, R is the (vectorial) residual function, the leapfrog class scheme implemented (see [3]) is:

$$U^{n+2}=U^n+2\mathrm{\Delta }t\cdot R(t^{n+1},U^{n+1})$$

Optionally, the Robert-Asselin-Williams (RAW) filter (see [3]) is applied to the computed integration steps:

$$\mathrm{\Delta }=\frac{\nu }{2}(U^n-2U^{n+1}+U^{n+2})$$$$U^{n+1}=U^{n+1}+\mathrm{\Delta }\ast \alpha$$$$U^{n+2}=U^{n+2}+\mathrm{\Delta }\ast (\alpha -1)$$

Note that for (\alpha=1) the filter reverts back to the standard Robert-Asselin scheme. The filter coefficients should be taken as (\nu \in (0,1]) and (\alpha \in (0.5,1]). The default values are

• (\nu=0.01)
• (\alpha=0.53)

@note The value of (\Delta t) must be provided, it not being computed by the integrator.

The schemes are explicit. The filter coefficients (\nu,,\alpha ) define the actual scheme.

Bibliography

[1] The integration of a low order spectral form of the primitive meteorological equations, Robert, A. J., J. Meteor. Soc. Japan,vol. 44, pages 237--245, 1966.

[2] Frequency filter for time integrations, Asselin, R., Monthly Weather Review, vol. 100, pages 487--490, 1972.

[3] The RAW filter: An improvement to the Robert–Asselin filter in semi-implicit integrations, Williams, P.D., Monthly Weather Review, vol. 139(6), pages 1996--2007, June 2011.

Source: src/app/prism/common/adam_prism_leapfrog_pic_object.F90

Dependencies

Contents

• prism_leapfrog_pic_object
• initialize
• load_from_file
• assign_step
• integrate
• description
• dotproduct
• crossproduct
• sq_norm

Variables

Name	Type	Attributes	Description
INI_SECTION_NAME	character(len=8)	parameter	INI (config) file section name containing time configs.

Derived Types

prism_leapfrog_pic_object

Leapfrog class definition.

Components

Name	Type	Attributes	Description
mpih	type(mpih_object)		MPI handler.
nu	real(kind=R8P)		Robert-Asselin filter coefficient.
alpha	real(kind=R8P)		Robert-Asselin-Williams filter coefficient.
is_filtered	logical		Flag to check if the integration if RAW filtered.
q_pic_old	real(kind=R8P)	allocatable	Pic variables, old time steps.
field	type(field_object)	pointer	The field.
grid	type(grid_object)	pointer	The grid.
ngc	integer(kind=I4P)	pointer	Number of ghost cells.
ni	integer(kind=I4P)	pointer	Number of cells in i direction.
nj	integer(kind=I4P)	pointer	Number of cells in j direction.
nk	integer(kind=I4P)	pointer	Number of cells in k direction.
nb	integer(kind=I4P)	pointer	Total blocks number for MPI.
blocks_number	integer(kind=I4P)	pointer	Actual blocks number.
ns	integer(kind=I4P)	pointer	Number of fluids specie.
nv	integer(kind=I4P)	pointer	Number of conservative variables.
pic	type(prism_pic_object)	pointer	The PIC object.
particle_number	integer(kind=I4P)	pointer	Number of particles.

Type-Bound Procedures

Name	Attributes	Description
assign_step	pass(self)	Assign q to old steps.
description	pass(self)	Return pretty-printed object description.
initialize	pass(self)	Initialize class.
integrate	pass(self)	Integrate.
load_from_file	pass(self)	Load config from file.

Subroutines

initialize

Initialize class.

subroutine initialize(self, file_parameters, scheme, grid, field, pic)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_leapfrog_pic_object)	inout		Leapfrog object.
file_parameters	type(file_ini)	in	optional	Simulation parameters ini file handler.
scheme	character(len=*)	in	optional	Runge-Kutta scheme.
grid	type(grid_object)	in	target	The grid.
field	type(field_object)	in	target	The field.
pic	type(prism_pic_object)	in	target	The PIC object.

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load_from_file

Load config from file.

subroutine load_from_file(self, file_parameters, go_on_fail)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_leapfrog_pic_object)	inout		Leapfrog object.
file_parameters	type(file_ini)	in		Simulation parameters ini file handler.
go_on_fail	logical	in	optional	Go on if load fails.

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assign_step

Assign q to leapfrog old step.

subroutine assign_step(self, s, q_pic, phi)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_leapfrog_pic_object)	inout		Leapfrog object.
s	integer(kind=I4P)	in		Current step number.
q_pic	real(kind=R8P)	in		Pic variables.
phi	real(kind=R8P)	in	optional	IB distance.

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integrate

Integrate.

subroutine integrate(self, dt, q_pic, pic_fields)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_leapfrog_pic_object)	inout		Leapfrog object.
dt	real(kind=R8P)	in		Time step.
q_pic	real(kind=R8P)	inout		Pic variables.
pic_fields	real(kind=R8P)	in		Fields value at particle locations.

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Functions

description

Return a pretty-formatted object description.

Attributes: pure

Returns: character(len=:)

function description(self) result(desc)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_leapfrog_pic_object)	in		Leapfrog object.

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dotproduct

Compute the scalar (dot) product.

Returns: real(kind=R8P)

function dotproduct(a, b) result(dot)

Arguments

Name	Type	Intent	Attributes	Description
a	real(kind=R8P)	in		Left hand side.
b	real(kind=R8P)	in		Left hand side.

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crossproduct

Returns: real(kind=R8P)

function crossproduct(a, b) result(cross)

Arguments

Name	Type	Intent	Attributes	Description
a	real(kind=R8P)	in		Left hand side.
b	real(kind=R8P)	in		Left hand side.

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sq_norm

Return the square of the norm of vector.

Returns: real(kind=R8P)

function sq_norm(a) result(sq)

Arguments

Name	Type	Intent	Attributes	Description
a	real(kind=R8P)	in		Input vector

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