coriolis_block_mod

Provides a derived type which representes the operator acting on velocity and its derivative with the Coriolis force. This can be used for preconditioning in the plume solver.

Uses

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Used by

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Variables

Type	Visibility	Attributes		Name		Initial
character(len=1),	private,	parameter	::	trans	=	'N'	The LAPACK parameter indicating not to operate on the transpose of the matrix when solving for boundary conditions.
type(uniform_scalar_field),	private		::	zero

Interfaces

public interface coriolis_block

private function constructor(phi, nu, velbound, dvelbound, integrate_bound, template) result(this)

Author: Chris MacMackin
Date: January 2018

Builds a Coriolis block which can be used to solve the inverse problem for the linear components of the plume momentum equations. The result can only be used with fields having the same grid as the template.

Arguments

Type	Intent		Name
real(kind=r8),	intent(in)	::	phi	The dimensionless coriolis parameter
real(kind=r8),	intent(in)	::	nu	The dimensionless eddy diffusivity
integer,	intent(in)	::	velbound	Location code for the velocity's boundary condition. 1 indicates upper boundary, -1 indicates lower boundary.
integer,	intent(in)	::	dvelbound	Location code for the velocity's boundary condition. 1 indicates upper boundary, -1 indicates lower boundary.
integer,	intent(in)	::	integrate_bound	Location code for the boundary to perform integrations from. This should be the opposite boundary from where boundary data is stored.
class(abstract_field),	intent(in)	::	template	A scalar field with the same grid as any fields passed as arguments to the solve_for method.

Return Value type(coriolis_block)

Derived Types

type, public :: coriolis_block

A data type representing a matrix operator for the momentum components of the linear parts plume equations, with the Coriolis force. It can be useful when preconditioning a the plume solver. It is inherently 1-D in its implementation, but has a transverse velocity component.

Components

Type	Visibility	Attributes		Name
real(kind=r8),	private,	dimension(4)	::	D_r	Real component of the diagonal matrix, $\bm{D}$ , with only diagonal values stored
real(kind=r8),	private,	dimension(4)	::	D_i	Imaginary component of the diagonal matrix, $\bm{D}$ , with only diagonal values stored
type(cheb1d_scalar_field),	private,	dimension(4,4)	::	emDxVinv_r	Real component of $e^{-\bm{D}x}\bm{V}^{-1}$
type(cheb1d_scalar_field),	private,	dimension(4,4)	::	emDxVinv_i	Imaginary component of $e^{-\bm{D}x}\bm{V}^{-1}$
type(cheb1d_scalar_field),	private,	dimension(4)	::	eDx_r	Real component of $e^{\bm{D}x}$ , with only diagonal values stored
type(cheb1d_scalar_field),	private,	dimension(4)	::	eDx_i	Imaginary component of $e^{\bm{D}x}$ , with only diagonal values stored
real(kind=r8),	private,	dimension(4,4)	::	V_r	Real component of the change of basis matrix, $\bm{V}$
real(kind=r8),	private,	dimension(4,4)	::	V_i	Imaginary component of the change of basis matrix, $\bm{V}$
type(pseudospec_block),	private		::	integrator	A pseudospectral differentiation block which can be used to perform integration
integer,	private		::	vel_bound_loc	Location code for the velocity's boundary condition
integer,	private		::	dvel_bound_loc	Location code for the velocity derivative's boundary condition
integer,	private		::	integrate_bound	Location from which to perform the integration
real(kind=r8),	private,	dimension(4)	::	xbounds	Boundary location for each component of the solution vector
complex(kind=r8),	private,	dimension(4,4)	::	bound_matrix	Matrix for the system to solve in order to satisfy the boundary conditions
complex(kind=r8),	private,	dimension(4,4)	::	bound_matrix_scaled	Matrix for the system to solve in order to satisfy the boundary conditions, which has been scaled by LAPACK95 to improve conditioning.
complex(kind=r8),	private,	dimension(4,4)	::	factored_matrix	Factored matrix for the system to solve in order to satisfy the boundary conditions
integer,	private,	dimension(4)	::	pivots	The pivots used in the factorisation of the matrix used to satisfy boundary conditions
real(kind=r8),	private,	dimension(4)	::	r_scales	Row scale factors from equilibrating the bound_matrix
real(kind=r8),	private,	dimension(4)	::	c_scales	Column scale factors from equilibrating the bound_matrix
character(len=1),	private		::	equed	The method used to equilibrate bound_matrix
integer,	private		::	int

Constructor

private function constructor(phi, nu, velbound, dvelbound, integrate_bound, template)	Builds a Coriolis block which can be used to solve the inverse problem for the linear components of the plume momentum equations. The result can only be used with fields having the same grid as the template.

Type-Bound Procedures

procedure, public :: solve_for
procedure, private :: assign
generic, public :: assignment(=) => assign

Functions

private function constructor(phi, nu, velbound, dvelbound, integrate_bound, template) result(this)

Author: Chris MacMackin
Date: January 2018

Arguments

Type	Intent		Name
real(kind=r8),	intent(in)	::	phi	The dimensionless coriolis parameter
real(kind=r8),	intent(in)	::	nu	The dimensionless eddy diffusivity
integer,	intent(in)	::	velbound	Location code for the velocity's boundary condition. 1 indicates upper boundary, -1 indicates lower boundary.
integer,	intent(in)	::	dvelbound	Location code for the velocity's boundary condition. 1 indicates upper boundary, -1 indicates lower boundary.
integer,	intent(in)	::	integrate_bound	Location code for the boundary to perform integrations from. This should be the opposite boundary from where boundary data is stored.
class(abstract_field),	intent(in)	::	template	A scalar field with the same grid as any fields passed as arguments to the solve_for method.

Return Value type(coriolis_block)

Subroutines

private subroutine solve_for(this, velocity, velocity_dx)

Author: Chris MacMackin
Date: January 2018

Inverts the linear portions of the plume momentum equation with the provided data. This is done by solving the linear ODE described in the documentation for the coriolis_block type. The block object must first have been initialised using the constructor.

Arguments

Type	Intent		Name
class(coriolis_block),	intent(inout)	::	this
class(vector_field),	intent(inout)	::	velocity	On input, the velocity value being preconditioned. On output, the preconditioned velocity.
class(vector_field),	intent(inout)	::	velocity_dx	On input, the velocity derivative being preconditioned. On output, the preconditioned velocity derivative.

private subroutine assign(this, rhs)

Author: Chris MacMackin
Date: January 2017

Safely assigns the value of one coriolis block to another.

Arguments

Type	Intent	Optional	Attributes		Name
class(coriolis_block),	intent(inout)			::	this
class(coriolis_block),	intent(in)			::	rhs	The value being assigned

coriolis_block_mod Module

Contents

Variables

Interfaces

Derived Types

Functions

Subroutines

Uses

Used by

Contents

Variables

Interfaces

Derived Types

Functions

Subroutines

Variables

Interfaces

public interface coriolis_block

private function constructor(phi, nu, velbound, dvelbound, integrate_bound, template) result(this)

Arguments

Return Value type(coriolis_block)

Derived Types

type, public :: coriolis_block

Components

Constructor

Type-Bound Procedures

Functions

private function constructor(phi, nu, velbound, dvelbound, integrate_bound, template) result(this)

Arguments

Return Value type(coriolis_block)

Subroutines

private subroutine solve_for(this, velocity, velocity_dx)

Arguments

private subroutine assign(this, rhs)

Arguments