integrand_ladvection

type, public, extends(integrand_tester_object) :: integrand_ladvection

1D linear advection field.

It is a FOODIE integrand class concrete extension.

1D linear advection field

The 1D linear advection equation is a conservation law that reads as $$ \begin{matrix} u_t = R(u) \Leftrightarrow u_t = F(u)_x \\ F(u) = a * u $$ where a is scalar constant coefficient. The PDE must completed with the proper initial and boundary conditions.

Numerical grid organization

The finite volume, Godunov's like approach is employed. The conservative variables (and the primitive ones) are co-located at the cell center. The cell and (inter)faces numeration is as follow.

                cell            (inter)faces
                 |                   |
                 v                   v
     |-------|-------|-.....-|-------|-------|-------|-------|-.....-|-------|-------|-------|-.....-|-------|-------|
     | 1-Ng  | 2-Ng  | ..... |  -1   |   0   |   1   |  2    | ..... |  Ni   | Ni+1  | Ni+2  | ..... |Ni+Ng-1| Ni+Ng |
     |-------|-------|-.....-|-------|-------|-------|-------|-.....-|-------|-------|-------|-.....-|-------|-------|
    0-Ng                             -1      0       1       2      Ni-1     Ni                                    Ni+Ng

Where Ni are the finite volumes (cells) used for discretizing the domain and Ng are the ghost cells used for imposing the left and right boundary conditions (for a total of 2Ng cells).

Inherited By

Help

Variables

CFL Dx Ng Ni a initial_state interpolator length u w_scheme weno_eps weno_order

Type-Bound Procedures

add_fast assign_integrand assign_real assignment(=) compute_dx description destroy dt error exact_solution export_tecplot impose_boundary_conditions initialize integrand_add_integrand integrand_add_integrand_fast integrand_add_real integrand_dimension integrand_multiply_integrand integrand_multiply_integrand_fast integrand_multiply_real integrand_multiply_real_scalar integrand_multiply_real_scalar_fast integrand_sub_integrand integrand_sub_real integrand_subtract_integrand_fast local_error multiply_fast operator(*) operator(+) operator(-) operator(.lterror.) output parse_cli real_add_integrand real_multiply_integrand real_scalar_multiply_integrand real_sub_integrand reconstruct_interfaces set_cli set_sin_wave_initial_state set_square_wave_initial_state subtract_fast t t_fast

Source Code

integrand_ladvection

Components

Type	Visibility	Attributes		Name		Initial
real(kind=R_P),	public		::	CFL	=	0._R_P	CFL value.
real(kind=R_P),	public		::	Dx	=	0._R_P	Space step.
integer(kind=I_P),	public		::	Ng	=	0	Ghost cells number.
integer(kind=I_P),	public		::	Ni	=	0	Space dimension.
real(kind=R_P),	public		::	a	=	0._R_P	Advection coefficient.
character(len=99),	public		::	initial_state			Initial state.
class(interpolator_object),	public,	allocatable	::	interpolator			WENO interpolator.
real(kind=R_P),	public		::	length	=	0._R_P	Domain length.
real(kind=R_P),	public,	allocatable	::	u(:)			Integrand (state) variable.
character(len=99),	public		::	w_scheme	=	''	WENO Scheme used.
real(kind=R_P),	public		::	weno_eps	=	0._R_P	WENO epsilon to avoid division by zero, default value.
integer(kind=I_P),	public		::	weno_order	=	0	WENO reconstruction order.

Type-Bound Procedures

generic, public :: add_fast => integrand_add_integrand_fast

Overloading add_fast method.

private pure subroutine integrand_add_integrand_fast(opr, lhs, rhs)

+ fast operator.

Arguments

Type	Intent		Name
class(integrand_oscillation),	intent(inout)	::	opr	Operator result.
class(integrand_object),	intent(in)	::	lhs	Left hand side.
class(integrand_object),	intent(in)	::	rhs	Right hand side.

procedure, public, pass(lhs) :: assign_integrand

= operator.

private subroutine assign_integrand(lhs, rhs)

= operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_ladvection),	intent(inout)			::	lhs	Left hand side.
class(integrand_object),	intent(in)			::	rhs	Right hand side.

procedure, public, pass(lhs) :: assign_real

= real operator.

private pure subroutine assign_real(lhs, rhs)

Assign one real to an advection field.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_ladvection),	intent(inout)			::	lhs	Left hand side.
real(kind=R_P),	intent(in)			::	rhs(1:)	Right hand side.

generic, public :: assignment(=) => assign_integrand, assign_real

Overloading = assignament.

private pure subroutine assign_integrand(lhs, rhs)

= operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(inout)			::	lhs	Left hand side.
class(integrand_object),	intent(in)			::	rhs	Right hand side.

private pure subroutine assign_real(lhs, rhs)

= real operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(inout)			::	lhs	Left hand side.
real(kind=R_P),	intent(in)			::	rhs(1:)	Right hand side.

procedure, public, pass(self) :: compute_dx

Compute the space step by means of CFL condition.

private pure function compute_dx(self, Dt) result(Dx)

Compute the space step step by means of CFL condition.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_ladvection),	intent(in)			::	self	Advection field.
real(kind=R_P),	intent(in)			::	Dt	Time step.

Return Value real(kind=R_P)

Space step.

procedure, public, pass(self) :: description

Return an informative description of the test.

private pure function description(self, prefix) result(desc)

Return informative integrator description.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_ladvection),	intent(in)			::	self	Integrand.
character(len=*),	intent(in),	optional		::	prefix	Prefixing string.

Return Value character(len=:), allocatable

Description.

procedure, public, pass(self) :: destroy

Destroy field.

private subroutine destroy(self)

Destroy field.

Arguments

Type Intent Optional Attributes Name

class(integrand_ladvection), intent(inout) :: self
Advection field.

procedure, public, pass(self) :: dt => compute_dt

Compute the current time step by means of CFL condition.

private pure function compute_dt(self, final_time, t) result(Dt)

Compute the current time step by means of CFL condition.

Arguments

Type	Intent	Optional		Name
class(integrand_ladvection),	intent(in)		::	self	Advection field.
real(kind=R_P),	intent(in)		::	final_time	Maximum integration time.
real(kind=R_P),	intent(in),	optional	::	t	Time.

Return Value real(kind=R_P)

Time step.

procedure, public, pass(self) :: error

Return error.

private pure function error(self, t, t0, U0)

Return error.

Arguments

Type	Intent	Optional		Name
class(integrand_ladvection),	intent(in)		::	self	Integrand.
real(kind=R_P),	intent(in)		::	t	Time.
real(kind=R_P),	intent(in),	optional	::	t0	Initial time.
class(integrand_object),	intent(in),	optional	::	U0	Initial conditions.

Return Value real(kind=R_P), allocatable, (:)

Error.

procedure, public, pass(self) :: exact_solution

Return exact solution.

private pure function exact_solution(self, t, t0, U0) result(exact)

Return exact solution.

Arguments

Type	Intent	Optional		Name
class(integrand_ladvection),	intent(in)		::	self	Integrand.
real(kind=R_P),	intent(in)		::	t	Time.
real(kind=R_P),	intent(in),	optional	::	t0	Initial time.
class(integrand_object),	intent(in),	optional	::	U0	Initial conditions.

Return Value real(kind=R_P), allocatable, (:)

Exact solution.

procedure, public, pass(self) :: export_tecplot

Export integrand to Tecplot file.

private subroutine export_tecplot(self, file_name, t, scheme, close_file, with_exact_solution, U0)

Export integrand to Tecplot file.

Arguments

Type	Intent	Optional		Name
class(integrand_ladvection),	intent(in)		::	self	Advection field.
character(len=*),	intent(in),	optional	::	file_name	File name.
real(kind=R_P),	intent(in),	optional	::	t	Time.
character(len=*),	intent(in),	optional	::	scheme	Scheme used to integrate integrand.
logical,	intent(in),	optional	::	close_file	Flag for closing file.
logical,	intent(in),	optional	::	with_exact_solution	Flag for export also exact solution.
class(integrand_object),	intent(in),	optional	::	U0	Initial conditions.

procedure, private, pass(self) :: impose_boundary_conditions

Impose boundary conditions.

private pure subroutine impose_boundary_conditions(self, u)

Impose boundary conditions.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_ladvection),	intent(in)			::	self	Advection field.
real(kind=R_P),	intent(inout)			::	u(1-self%Ng:)	Conservative variables.

procedure, public, pass(self) :: initialize

Initialize integrand.

private subroutine initialize(self, Dt)

Initialize integrand.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_ladvection),	intent(inout)			::	self	Integrand.
real(kind=R_P),	intent(in)			::	Dt	Time step.

procedure, public, pass(lhs) :: integrand_add_integrand

+ operator.

private pure function integrand_add_integrand(lhs, rhs) result(opr)

+ operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_ladvection),	intent(in)			::	lhs	Left hand side.
class(integrand_object),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

procedure, public, pass(opr) :: integrand_add_integrand_fast

+ fast operator.

private pure subroutine integrand_add_integrand_fast(opr, lhs, rhs)

+ fast operator.

Arguments

Type	Intent		Name
class(integrand_object),	intent(inout)	::	opr	Operator result.
class(integrand_object),	intent(in)	::	lhs	Left hand side.
class(integrand_object),	intent(in)	::	rhs	Right hand side.

procedure, public, pass(lhs) :: integrand_add_real

+ real operator.

private pure function integrand_add_real(lhs, rhs) result(opr)

+ real operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_ladvection),	intent(in)			::	lhs	Left hand side.
real(kind=R_P),	intent(in)			::	rhs(1:)	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

procedure, public, pass(self) :: integrand_dimension

Return integrand dimension.

private pure function integrand_dimension(self)

return integrand dimension.

Arguments

Type Intent Optional Attributes Name

class(integrand_ladvection), intent(in) :: self
integrand.

Return Value integer(kind=I_P)

integrand dimension.

Type	Intent	Optional	Attributes		Name
class(integrand_ladvection),	intent(in)			::	self	integrand.

procedure, public, pass(lhs) :: integrand_multiply_integrand

* operator.

private pure function integrand_multiply_integrand(lhs, rhs) result(opr)

* operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_ladvection),	intent(in)			::	lhs	Left hand side.
class(integrand_object),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

procedure, public, pass(opr) :: integrand_multiply_integrand_fast

* fast operator.

private pure subroutine integrand_multiply_integrand_fast(opr, lhs, rhs)

* fast operator.

Arguments

Type	Intent		Name
class(integrand_object),	intent(inout)	::	opr	Operator result.
class(integrand_object),	intent(in)	::	lhs	Left hand side.
class(integrand_object),	intent(in)	::	rhs	Right hand side.

procedure, public, pass(lhs) :: integrand_multiply_real

* real operator.

private pure function integrand_multiply_real(lhs, rhs) result(opr)

* real_scalar operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_ladvection),	intent(in)			::	lhs	Left hand side.
real(kind=R_P),	intent(in)			::	rhs(1:)	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

procedure, public, pass(lhs) :: integrand_multiply_real_scalar

* real_scalar operator.

private pure function integrand_multiply_real_scalar(lhs, rhs) result(opr)

* real_scalar operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_ladvection),	intent(in)			::	lhs	Left hand side.
real(kind=R_P),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

procedure, public, pass(opr) :: integrand_multiply_real_scalar_fast

* real_scalar fast operator.

private pure subroutine integrand_multiply_real_scalar_fast(opr, lhs, rhs)

* real_scalar fast operator.

Arguments

Type	Intent		Name
class(integrand_object),	intent(inout)	::	opr	Operator result.
class(integrand_object),	intent(in)	::	lhs	Left hand side.
real(kind=R_P),	intent(in)	::	rhs	Right hand side.

procedure, public, pass(lhs) :: integrand_sub_integrand

- operator.

private pure function integrand_sub_integrand(lhs, rhs) result(opr)

- operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_ladvection),	intent(in)			::	lhs	Left hand side.
class(integrand_object),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

procedure, public, pass(lhs) :: integrand_sub_real

- real operator.

private pure function integrand_sub_real(lhs, rhs) result(opr)

- real operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_ladvection),	intent(in)			::	lhs	Left hand side.
real(kind=R_P),	intent(in)			::	rhs(1:)	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

procedure, public, pass(opr) :: integrand_subtract_integrand_fast

- fast operator.

private pure subroutine integrand_subtract_integrand_fast(opr, lhs, rhs)

- fast operator.

Arguments

Type	Intent		Name
class(integrand_object),	intent(inout)	::	opr	Operator result.
class(integrand_object),	intent(in)	::	lhs	Left hand side.
class(integrand_object),	intent(in)	::	rhs	Right hand side.

procedure, public, pass(lhs) :: local_error

||integrand_ladvection - integrand_ladvection|| operator.

private function local_error(lhs, rhs) result(error)

Estimate local truncation error between 2 advection approximations.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_ladvection),	intent(in)			::	lhs	Left hand side.
class(integrand_object),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P)

Error estimation.

generic, public :: multiply_fast => integrand_multiply_integrand_fast, integrand_multiply_real_scalar_fast

Overloading multiply_fast method.

private pure subroutine integrand_multiply_integrand_fast(opr, lhs, rhs)

* fast operator.

Arguments

Type	Intent		Name
class(integrand_oscillation),	intent(inout)	::	opr	Operator result.
class(integrand_object),	intent(in)	::	lhs	Left hand side.
class(integrand_object),	intent(in)	::	rhs	Right hand side.

private pure subroutine integrand_multiply_real_scalar_fast(opr, lhs, rhs)

* real_scalar fast operator.

Arguments

Type	Intent		Name
class(integrand_oscillation),	intent(inout)	::	opr	Operator result.
class(integrand_object),	intent(in)	::	lhs	Left hand side.
real(kind=R_P),	intent(in)	::	rhs	Right hand side.

generic, public :: **operator(*)** => integrand_multiply_integrand, integrand_multiply_real, real_multiply_integrand, integrand_multiply_real_scalar, real_scalar_multiply_integrand

Overloading * operator.

private pure function integrand_multiply_integrand(lhs, rhs) result(opr)

* operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	lhs	Left hand side.
class(integrand_object),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

private pure function integrand_multiply_real(lhs, rhs) result(opr)

* real_scalar operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	lhs	Left hand side.
real(kind=R_P),	intent(in)			::	rhs(1:)	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

private pure function real_multiply_integrand(lhs, rhs) result(opr)

real_scalar * operator.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=R_P),	intent(in)			::	lhs(1:)	Left hand side.
class(integrand_oscillation),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

private pure function integrand_multiply_real_scalar(lhs, rhs) result(opr)

* real_scalar operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	lhs	Left hand side.
real(kind=R_P),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

private pure function real_scalar_multiply_integrand(lhs, rhs) result(opr)

real_scalar * operator.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=R_P),	intent(in)			::	lhs	Left hand side.
class(integrand_oscillation),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

generic, public :: operator(+) => integrand_add_integrand, integrand_add_real, real_add_integrand

Overloading + operator.

private pure function integrand_add_integrand(lhs, rhs) result(opr)

+ operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	lhs	Left hand side.
class(integrand_object),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

private pure function integrand_add_real(lhs, rhs) result(opr)

+ real operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	lhs	Left hand side.
real(kind=R_P),	intent(in)			::	rhs(1:)	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

private pure function real_add_integrand(lhs, rhs) result(opr)

real + operator.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=R_P),	intent(in)			::	lhs(1:)	Left hand side.
class(integrand_oscillation),	intent(in)			::	rhs	Left hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

generic, public :: operator(-) => integrand_sub_integrand, integrand_sub_real, real_sub_integrand

Overloading - operator.

private pure function integrand_sub_integrand(lhs, rhs) result(opr)

- operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	lhs	Left hand side.
class(integrand_object),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

private pure function integrand_sub_real(lhs, rhs) result(opr)

- real operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	lhs	Left hand side.
real(kind=R_P),	intent(in)			::	rhs(1:)	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

private pure function real_sub_integrand(lhs, rhs) result(opr)

real - operator.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=R_P),	intent(in)			::	lhs(1:)	Left hand side.
class(integrand_oscillation),	intent(in)			::	rhs	Left hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

generic, public :: operator(.lterror.) => local_error

Estimate local truncation error.

private pure function local_error(lhs, rhs) result(error)

Estimate local truncation error between 2 oscillation approximations.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	lhs	Left hand side.
class(integrand_object),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P)

Error estimation.

procedure, public, pass(self) :: output

Extract integrand state field.

private pure function output(self) result(state)

Output the advection field state.

Arguments

Type Intent Optional Attributes Name

class(integrand_ladvection), intent(in) :: self
Advection field.

Return Value real(kind=R_P), allocatable, (:)

Advection state

procedure, public, pass(self) :: parse_cli

Initialize from command line interface.

private subroutine parse_cli(self, cli)

Initialize from command line interface.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_ladvection),	intent(inout)			::	self	Advection field.
type(command_line_interface),	intent(inout)			::	cli	Command line interface handler.

procedure, public, pass(rhs) :: real_add_integrand

real + operator.

private pure function real_add_integrand(lhs, rhs) result(opr)

real + operator.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=R_P),	intent(in)			::	lhs(1:)	Left hand side.
class(integrand_ladvection),	intent(in)			::	rhs	Left hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

procedure, public, pass(rhs) :: real_multiply_integrand

real * operator.

private pure function real_multiply_integrand(lhs, rhs) result(opr)

real_scalar * operator.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=R_P),	intent(in)			::	lhs(1:)	Left hand side.
class(integrand_ladvection),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

procedure, public, pass(rhs) :: real_scalar_multiply_integrand

real_scalar * operator.

private pure function real_scalar_multiply_integrand(lhs, rhs) result(opr)

real_scalar * operator.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=R_P),	intent(in)			::	lhs	Left hand side.
class(integrand_ladvection),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

procedure, public, pass(rhs) :: real_sub_integrand

real - operator.

private pure function real_sub_integrand(lhs, rhs) result(opr)

real - operator.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=R_P),	intent(in)			::	lhs(1:)	Left hand side.
class(integrand_ladvection),	intent(in)			::	rhs	Left hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

procedure, private, pass(self) :: reconstruct_interfaces

Reconstruct interface states.

private subroutine reconstruct_interfaces(self, conservative, r_conservative)

Reconstruct interfaces states.

Arguments

Type	Intent		Name
class(integrand_ladvection),	intent(in)	::	self	Advection field.
real(kind=R_P),	intent(in)	::	conservative(1-self%Ng:)	Conservative variables.
real(kind=R_P),	intent(inout)	::	r_conservative(1:,0:)	Reconstructed conservative vars.

procedure, public, nopass :: set_cli

Set command line interface.

private subroutine set_cli(cli)

Set command line interface.

Arguments

Type Intent Optional Attributes Name

type(command_line_interface), intent(inout) :: cli
Command line interface handler.

Type	Intent	Optional	Attributes		Name
type(command_line_interface),	intent(inout)			::	cli	Command line interface handler.

procedure, private, pass(self) :: set_sin_wave_initial_state

Set initial state as a sin wave.

private subroutine set_sin_wave_initial_state(self)

Set initial state as a sin wave.

Arguments

Type Intent Optional Attributes Name

class(integrand_ladvection), intent(inout) :: self
Advection field.

procedure, private, pass(self) :: set_square_wave_initial_state

Set initial state as a square wave.

private subroutine set_square_wave_initial_state(self)

Set initial state as a square wave.

Arguments

Type Intent Optional Attributes Name

class(integrand_ladvection), intent(inout) :: self
Advection field.

generic, public :: subtract_fast => integrand_subtract_integrand_fast

Overloading subtract_fast method.

private pure subroutine integrand_subtract_integrand_fast(opr, lhs, rhs)

- fast operator.

Arguments

Type	Intent		Name
class(integrand_oscillation),	intent(inout)	::	opr	Operator result.
class(integrand_object),	intent(in)	::	lhs	Left hand side.
class(integrand_object),	intent(in)	::	rhs	Right hand side.

procedure, public, pass(self) :: t => dU_dt

Time derivative, residuals.

private function dU_dt(self, t) result(dState_dt)

Time derivative of advection field, the residuals function.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_ladvection),	intent(in)			::	self	Advection field.
real(kind=R_P),	intent(in),	optional		::	t	Time.

Return Value real(kind=R_P), allocatable, (:)

Advection field time derivative.

procedure, public, pass(self) :: t_fast

Time derivative, residuals, fast mode.

private subroutine t_fast(self, t)

Time derivative function of integrand class, i.e. the residuals function. Fast mode acting directly on self.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_object),	intent(inout)			::	self	Integrand field.
real(kind=R_P),	intent(in),	optional		::	t	Time.

Source Code

type, extends(integrand_tester_object) :: integrand_ladvection
   !< 1D linear advection field.
   !<
   !< It is a FOODIE integrand class concrete extension.
   !<
   !<### 1D linear advection field
   !< The 1D linear advection equation is a conservation law that reads as
   !<$$
   !<\begin{matrix}
   !<u_t = R(u)  \Leftrightarrow u_t = F(u)_x \\
   !<F(u) = a * u
   !<$$
   !< where `a` is scalar constant coefficient. The PDE must completed with the proper initial and boundary conditions.
   !<
   !<#### Numerical grid organization
   !< The finite volume, Godunov's like approach is employed. The conservative variables (and the primitive ones) are co-located at
   !< the cell center. The cell and (inter)faces numeration is as follow.
   !<```
   !<                cell            (inter)faces
   !<                 |                   |
   !<                 v                   v
   !<     |-------|-------|-.....-|-------|-------|-------|-------|-.....-|-------|-------|-------|-.....-|-------|-------|
   !<     | 1-Ng  | 2-Ng  | ..... |  -1   |   0   |   1   |  2    | ..... |  Ni   | Ni+1  | Ni+2  | ..... |Ni+Ng-1| Ni+Ng |
   !<     |-------|-------|-.....-|-------|-------|-------|-------|-.....-|-------|-------|-------|-.....-|-------|-------|
   !<    0-Ng                             -1      0       1       2      Ni-1     Ni                                    Ni+Ng
   !<```
   !< Where *Ni* are the finite volumes (cells) used for discretizing the domain and *Ng* are the ghost cells used for imposing the
   !< left and right boundary conditions (for a total of *2Ng* cells).
   character(99)                           :: w_scheme=''     !< WENO Scheme used.
   integer(I_P)                            :: weno_order=0    !< WENO reconstruction order.
   real(R_P)                               :: weno_eps=0._R_P !< WENO epsilon to avoid division by zero, default value.
   real(R_P)                               :: CFL=0._R_P      !< CFL value.
   integer(I_P)                            :: Ni=0            !< Space dimension.
   integer(I_P)                            :: Ng=0            !< Ghost cells number.
   real(R_P)                               :: length=0._R_P   !< Domain length.
   real(R_P)                               :: Dx=0._R_P       !< Space step.
   real(R_P)                               :: a=0._R_P        !< Advection coefficient.
   real(R_P), allocatable                  :: u(:)            !< Integrand (state) variable.
   class(interpolator_object), allocatable :: interpolator    !< WENO interpolator.
   character(99)                           :: initial_state   !< Initial state.
   contains
      ! auxiliary methods
      procedure, pass(self), public :: destroy          !< Destroy field.
      procedure, pass(self), public :: dt => compute_dt !< Compute the current time step by means of CFL condition.
      procedure, pass(self), public ::       compute_dx !< Compute the space step by means of CFL condition.
      procedure, pass(self), public :: output           !< Extract integrand state field.
      ! integrand_tester_object deferred methods
      procedure, pass(self), public :: description    !< Return an informative description of the test.
      procedure, pass(self), public :: error          !< Return error.
      procedure, pass(self), public :: exact_solution !< Return exact solution.
      procedure, pass(self), public :: export_tecplot !< Export integrand to Tecplot file.
      procedure, pass(self), public :: initialize     !< Initialize integrand.
      procedure, pass(self), public :: parse_cli      !< Initialize from command line interface.
      procedure, nopass,     public :: set_cli        !< Set command line interface.
      ! integrand_object deferred methods
      procedure, pass(self), public :: integrand_dimension !< Return integrand dimension.
      procedure, pass(self), public :: t => dU_dt          !< Time derivative, residuals.
      ! operators
      procedure, pass(lhs), public :: local_error !<`||integrand_ladvection - integrand_ladvection||` operator.
      ! +
      procedure, pass(lhs), public :: integrand_add_integrand !< `+` operator.
      procedure, pass(lhs), public :: integrand_add_real      !< `+ real` operator.
      procedure, pass(rhs), public :: real_add_integrand      !< `real +` operator.
      ! *
      procedure, pass(lhs), public :: integrand_multiply_integrand   !< `*` operator.
      procedure, pass(lhs), public :: integrand_multiply_real        !< `* real` operator.
      procedure, pass(rhs), public :: real_multiply_integrand        !< `real *` operator.
      procedure, pass(lhs), public :: integrand_multiply_real_scalar !< `* real_scalar` operator.
      procedure, pass(rhs), public :: real_scalar_multiply_integrand !< `real_scalar *` operator.
      ! -
      procedure, pass(lhs), public :: integrand_sub_integrand !< `-` operator.
      procedure, pass(lhs), public :: integrand_sub_real      !< `- real` operator.
      procedure, pass(rhs), public :: real_sub_integrand      !< `real -` operator.
      ! =
      procedure, pass(lhs), public :: assign_integrand !< `=` operator.
      procedure, pass(lhs), public :: assign_real      !< `= real` operator.
      ! override fast operators
      ! procedure, pass(self), public :: t_fast                              !< Time derivative, residuals, fast mode.
      ! procedure, pass(opr),  public :: integrand_add_integrand_fast        !< `+` fast operator.
      ! procedure, pass(opr),  public :: integrand_multiply_integrand_fast   !< `*` fast operator.
      ! procedure, pass(opr),  public :: integrand_multiply_real_scalar_fast !< `* real_scalar` fast operator.
      ! procedure, pass(opr),  public :: integrand_subtract_integrand_fast   !< `-` fast operator.
      ! private methods
      procedure, pass(self), private :: impose_boundary_conditions    !< Impose boundary conditions.
      procedure, pass(self), private :: reconstruct_interfaces        !< Reconstruct interface states.
      procedure, pass(self), private :: set_sin_wave_initial_state    !< Set initial state as a sin wave.
      procedure, pass(self), private :: set_square_wave_initial_state !< Set initial state as a square wave.
endtype integrand_ladvection

integrand_ladvection Derived Type

Variables

Type-Bound Procedures

Source Code

All Derived Types

type, public, extends(integrand_tester_object) :: integrand_ladvection

1D linear advection field

Numerical grid organization

Inherited By

Variables

Type-Bound Procedures

Source Code

Components

Type-Bound Procedures

generic, public :: add_fast => integrand_add_integrand_fast

private pure subroutine integrand_add_integrand_fast(opr, lhs, rhs)

Arguments

procedure, public, pass(lhs) :: assign_integrand

private subroutine assign_integrand(lhs, rhs)

Arguments

procedure, public, pass(lhs) :: assign_real

private pure subroutine assign_real(lhs, rhs)

Arguments

generic, public :: assignment(=) => assign_integrand, assign_real

private pure subroutine assign_integrand(lhs, rhs)

Arguments

private pure subroutine assign_real(lhs, rhs)

Arguments

procedure, public, pass(self) :: compute_dx

private pure function compute_dx(self, Dt) result(Dx)

Arguments

Return Value real(kind=R_P)

procedure, public, pass(self) :: description

private pure function description(self, prefix) result(desc)

Arguments

Return Value character(len=:), allocatable

procedure, public, pass(self) :: destroy

private subroutine destroy(self)

Arguments

procedure, public, pass(self) :: dt => compute_dt

private pure function compute_dt(self, final_time, t) result(Dt)

Arguments

Return Value real(kind=R_P)

procedure, public, pass(self) :: error

private pure function error(self, t, t0, U0)

Arguments

Return Value real(kind=R_P), allocatable, (:)

procedure, public, pass(self) :: exact_solution

private pure function exact_solution(self, t, t0, U0) result(exact)

Arguments

Return Value real(kind=R_P), allocatable, (:)

procedure, public, pass(self) :: export_tecplot

private subroutine export_tecplot(self, file_name, t, scheme, close_file, with_exact_solution, U0)

Arguments

procedure, private, pass(self) :: impose_boundary_conditions

private pure subroutine impose_boundary_conditions(self, u)

Arguments

procedure, public, pass(self) :: initialize

private subroutine initialize(self, Dt)

Arguments

procedure, public, pass(lhs) :: integrand_add_integrand

private pure function integrand_add_integrand(lhs, rhs) result(opr)

Arguments

Return Value real(kind=R_P), allocatable, (:)

procedure, public, pass(opr) :: integrand_add_integrand_fast

private pure subroutine integrand_add_integrand_fast(opr, lhs, rhs)

Arguments

procedure, public, pass(lhs) :: integrand_add_real

private pure function integrand_add_real(lhs, rhs) result(opr)

Arguments

Return Value real(kind=R_P), allocatable, (:)

procedure, public, pass(self) :: integrand_dimension

private pure function integrand_dimension(self)

Arguments

Return Value integer(kind=I_P)

procedure, public, pass(lhs) :: integrand_multiply_integrand

private pure function integrand_multiply_integrand(lhs, rhs) result(opr)

Arguments

Return Value real(kind=R_P), allocatable, (:)

procedure, public, pass(opr) :: integrand_multiply_integrand_fast

generic, public :: **operator(*)** => integrand_multiply_integrand, integrand_multiply_real, real_multiply_integrand, integrand_multiply_real_scalar, real_scalar_multiply_integrand