type_euler_1D – FOODIE

Uses:
foodie
penf
wenoof

Define Euler 1D field that is a concrete extension of the abstract integrand type.

Used By

Derived Types

euler_1D

Functions

E H a add_euler compute_dt conservative2primitive dEuler_dt euler_local_error euler_multiply_euler euler_multiply_real output p previous_step primitive2conservative r real_multiply_euler sub_euler

Subroutines

compute_inter_states destroy euler_assign_euler euler_assign_real impose_boundary_conditions init reconstruct_interfaces_states riemann_solver update_previous_steps

Derived Types

type, public, extends(integrand) :: euler_1D

Euler 1D PDEs system field.

Components

Type	Visibility	Attributes		Name		Initial
character(len=:),	private,	allocatable	::	BC_L			Left boundary condition type.
character(len=:),	private,	allocatable	::	BC_R			Right boundary condition type.
real(kind=R_P),	private		::	Dx	=	0._R_P	Space step.
integer(kind=I_P),	private		::	Nc	=	0	Number of conservative variables, Ns+2.
integer(kind=I_P),	private		::	Ng	=	0	Number of ghost cells for boundary conditions handling.
integer(kind=I_P),	private		::	Ni	=	0	Space dimension.
integer(kind=I_P),	private		::	Np	=	0	Number of primitive variables, Ns+4.
integer(kind=I_P),	private		::	Ns	=	0	Number of initial species.
real(kind=R_P),	private,	allocatable	::	U(:,:)			Integrand (state) variables, whole physical domain [1:Nc,1-Ng:Ni+Ng].
real(kind=R_P),	private,	allocatable	::	cp0(:)			Specific heat cp of initial species [1:Ns].
real(kind=R_P),	private,	allocatable	::	cv0(:)			Specific heat cv of initial species [1:Ns].
integer(kind=I_P),	private		::	ord	=	0	Space accuracy formal order.
real(kind=R_P),	private,	allocatable	::	previous(:,:,:)			Previous time steps states [1:Nc,1-Ng:Ni+Ng,1:steps].
integer(kind=I_P),	private		::	steps	=	0	Number of time steps stored.
type(weno_interpolator_upwind),	private		::	weno			WENO interpolator.

Type-Bound Procedures

procedure, public, pass(lhs) :: add => add_euler	Euler + Euler operator.
procedure, public, pass(lhs) :: assign_integrand => euler_assign_euler	Euler = Euler.
procedure, public, pass(lhs) :: assign_real => euler_assign_real	Euler = real.
procedure, private, pass(self) :: conservative2primitive	Convert conservative variables to primitive ones.
procedure, public, pass(self) :: destroy	Destroy field.
procedure, public, pass(self) :: dt => compute_dt	Compute the current time step, by means of CFL condition.
procedure, private, pass(self) :: impose_boundary_conditions	Impose boundary conditions.
procedure, public, pass(self) :: init	Init field.
procedure, public, pass(lhs) :: integrand_multiply_integrand => euler_multiply_euler	Euler * Euler operator.
procedure, public, pass(lhs) :: integrand_multiply_real => euler_multiply_real	Euler * real operator.
procedure, public, pass(lhs) :: local_error => euler_local_error	Local error.
procedure, public, pass(self) :: output	Extract Euler field.
procedure, public, pass(self) :: previous_step	Get a previous time step.
procedure, private, pass(self) :: primitive2conservative	Convert primitive variables to conservative ones.
procedure, public, pass(rhs) :: real_multiply_integrand => real_multiply_euler	Real * Euler operator.
procedure, private, pass(self) :: reconstruct_interfaces_states	Reconstruct interfaces states.
procedure, private, pass(self) :: riemann_solver	Solve the Riemann Problem at cell interfaces.
procedure, public, pass(lhs) :: sub => sub_euler	Euler - Euler.
procedure, public, pass(self) :: t => dEuler_dt	Time derivative, residuals function.
procedure, public, pass(self) :: update_previous_steps	Update previous time steps.

Functions

private elemental function E(p, r, u, g) result(energy)

Compute total specific energy (per unit of mass). $$ E = \frac{p}{{\left( {\g - 1} \right)\r }} + \frac{{u^2 }}{2} $$

Arguments

Type	Intent		Name
real(kind=R_P),	intent(in)	::	p	Pressure.
real(kind=R_P),	intent(in)	::	r	Density.
real(kind=R_P),	intent(in)	::	u	Module of velocity vector.
real(kind=R_P),	intent(in)	::	g	Specific heats ratio $\frac{{c_p}}{{c_v}}$.

Return Value real(kind=R_P)

Total specific energy (per unit of mass).

private elemental function H(p, r, u, g) result(entalpy)

Compute total specific entalpy (per unit of mass). $$ H = \frac{{\g p}}{{\left( {\g - 1} \right)\r }} + \frac{{u^2 }}{2} $$

Arguments

Type	Intent		Name
real(kind=R_P),	intent(in)	::	p	Pressure.
real(kind=R_P),	intent(in)	::	r	Density.
real(kind=R_P),	intent(in)	::	u	Module of velocity vector.
real(kind=R_P),	intent(in)	::	g	Specific heats ratio $\frac{{c_p}}{{c_v}}$.

Return Value real(kind=R_P)

Total specific entalpy (per unit of mass).

private elemental function a(p, r, g) result(ss)

Compute the speed of sound for an ideal calorically perfect gas.

Arguments

Type	Intent		Name
real(kind=R_P),	intent(in)	::	p	Pressure.
real(kind=R_P),	intent(in)	::	r	Density.
real(kind=R_P),	intent(in)	::	g	Specific heats ratio $\frac{{c_p}}{{c_v}}$.

Return Value real(kind=R_P)

Speed of sound.

private function add_euler(lhs, rhs) result(opr)

Add two Euler fields.

Arguments

Type	Intent	Optional	Attributes		Name
class(euler_1D),	intent(in)			::	lhs	Left hand side.
class(integrand),	intent(in)			::	rhs	Right hand side.

Return Value class(integrand), allocatable

Operator result.

private pure function compute_dt(self, Nmax, Tmax, t, CFL) result(Dt)

Compute the current time step by means of CFL condition.

Arguments

Type	Intent		Name
class(euler_1D),	intent(in)	::	self	Euler field.
integer(kind=I_P),	intent(in)	::	Nmax	Maximun number of iterates.
real(kind=R_P),	intent(in)	::	Tmax	Maximum time (ignored if Nmax>0).
real(kind=R_P),	intent(in)	::	t	Time.
real(kind=R_P),	intent(in)	::	CFL	CFL value.

Return Value real(kind=R_P)

Time step.

private pure function conservative2primitive(self, conservative) result(primitive)

Convert conservative variables to primitive variables.

Arguments

Type	Intent	Optional	Attributes		Name
class(euler_1D),	intent(in)			::	self	Euler field.
real(kind=R_P),	intent(in)			::	conservative(:)	Conservative variables.

Return Value real(kind=R_P) (1:self%Np)

Primitive variables.

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

Time derivative of Euler field, the residuals function.

Arguments

Type	Intent	Optional	Attributes		Name
class(euler_1D),	intent(in)			::	self	Euler field.
real(kind=R_P),	intent(in),	optional		::	t	Time.

Return Value class(integrand), allocatable

Euler field time derivative.

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

Estimate local truncation error between 2 euler approximations.

Arguments

Type	Intent	Optional	Attributes		Name
class(euler_1D),	intent(in)			::	lhs	Left hand side.
class(integrand),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P)

Error estimation.

private function euler_multiply_euler(lhs, rhs) result(opr)

Multiply an Euler field by another one.

Arguments

Type	Intent	Optional	Attributes		Name
class(euler_1D),	intent(in)			::	lhs	Left hand side.
class(integrand),	intent(in)			::	rhs	Right hand side.

Return Value class(integrand), allocatable

Operator result.

private function euler_multiply_real(lhs, rhs) result(opr)

Multiply an Euler field by a real scalar.

Arguments

Type	Intent	Optional	Attributes		Name
class(euler_1D),	intent(in)			::	lhs	Left hand side.
real(kind=R_P),	intent(in)			::	rhs	Right hand side.

Return Value class(integrand), allocatable

Operator result.

private pure function output(self) result(state)

Output the Euler field state (primitive variables).

Arguments

Type	Intent	Optional	Attributes		Name
class(euler_1D),	intent(in)			::	self	Euler field.

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

Euler state vector.

private elemental function p(r, a, g) result(pressure)

Compute the pressure for an ideal calorically perfect gas.

Arguments

Type	Intent		Name
real(kind=R_P),	intent(in)	::	r	Density.
real(kind=R_P),	intent(in)	::	a	Speed of sound.
real(kind=R_P),	intent(in)	::	g	Specific heats ratio $\frac{{c_p}}{{c_v}}$.

Return Value real(kind=R_P)

Pressure.

private function previous_step(self, n) result(previous)

Extract previous time solution of Euler field.

Arguments

Type	Intent	Optional	Attributes		Name
class(euler_1D),	intent(in)			::	self	Euler field.
integer(kind=I_P),	intent(in)			::	n	Time level.

Return Value class(integrand), allocatable

Previous time solution of Euler field.

private pure function primitive2conservative(self, primitive) result(conservative)

Convert primitive variables to conservative variables.

Arguments

Type	Intent	Optional	Attributes		Name
class(euler_1D),	intent(in)			::	self	Euler field.
real(kind=R_P),	intent(in)			::	primitive(:)	Primitive variables.

Return Value real(kind=R_P) (1:self%Nc)

Conservative variables.

private elemental function r(p, a, g) result(density)

Compute the density for an ideal calorically perfect gas.

Arguments

Type	Intent		Name
real(kind=R_P),	intent(in)	::	p	Pressure.
real(kind=R_P),	intent(in)	::	a	Speed of sound.
real(kind=R_P),	intent(in)	::	g	Specific heats ratio $\frac{{c_p}}{{c_v}}$.

Return Value real(kind=R_P)

Density.

private function real_multiply_euler(lhs, rhs) result(opr)

Multiply a real scalar by an Euler field.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=R_P),	intent(in)			::	lhs	Left hand side.
class(euler_1D),	intent(in)			::	rhs	Right hand side.

Return Value class(integrand), allocatable

Operator result.

private function sub_euler(lhs, rhs) result(opr)

Subtract two Euler fields.

Arguments

Type	Intent	Optional	Attributes		Name
class(euler_1D),	intent(in)			::	lhs	Left hand side.
class(integrand),	intent(in)			::	rhs	Right hand side.

Return Value class(integrand), allocatable

Operator result.

Subroutines

private pure subroutine compute_inter_states(r1, p1, u1, g1, r4, p4, u4, g4, p, S, S1, S4)

Compute inter states (23*-states) from state1 and state4.

Arguments

Type	Intent		Name
real(kind=R_P),	intent(in)	::	r1	Density of state 1.
real(kind=R_P),	intent(in)	::	p1	Pressure of state 1.
real(kind=R_P),	intent(in)	::	u1	Velocity of state 1.
real(kind=R_P),	intent(in)	::	g1	Specific heat ratio of state 1.
real(kind=R_P),	intent(in)	::	r4	Density of state 4.
real(kind=R_P),	intent(in)	::	p4	Pressure of state 4.
real(kind=R_P),	intent(in)	::	u4	Velocity of state 4.
real(kind=R_P),	intent(in)	::	g4	Specific heat ratio of state 4.
real(kind=R_P),	intent(out)	::	p	Pressure of the intermediate states.
real(kind=R_P),	intent(out)	::	S	Contact discontinuity signal velocity.
real(kind=R_P),	intent(out)	::	S1	Left fastest signal velocity.
real(kind=R_P),	intent(out)	::	S4	Right fastest signal velocity.

private pure subroutine destroy(self)

Destroy field.

Arguments

Type	Intent	Optional	Attributes		Name
class(euler_1D),	intent(inout)			::	self	Euler field.

private subroutine euler_assign_euler(lhs, rhs)

Assign one Euler field to another.

Arguments

Type	Intent	Optional	Attributes		Name
class(euler_1D),	intent(inout)			::	lhs	Left hand side.
class(integrand),	intent(in)			::	rhs	Right hand side.

private subroutine euler_assign_real(lhs, rhs)

Assign one real to an Euler field.

Arguments

Type	Intent	Optional	Attributes		Name
class(euler_1D),	intent(inout)			::	lhs	Left hand side.
real(kind=R_P),	intent(in)			::	rhs	Right hand side.

private pure subroutine impose_boundary_conditions(self, primitive)

Impose boundary conditions.

Arguments

Type	Intent	Optional	Attributes		Name
class(euler_1D),	intent(in)			::	self	Euler field.
real(kind=R_P),	intent(inout)			::	primitive(1:self%Np,1-self%Ng:self%Ni+self%Ng)	Primitive variables [1:Np,1-Ng:Ni+Ng].

private subroutine init(self, Ni, Ns, Dx, BC_L, BC_R, initial_state, cp0, cv0, steps, ord)

Init field.

Arguments

Type	Intent	Optional		Name
class(euler_1D),	intent(inout)		::	self	Euler field.
integer(kind=I_P),	intent(in)		::	Ni	Space dimension.
integer(kind=I_P),	intent(in)		::	Ns	Number of initial species.
real(kind=R_P),	intent(in)		::	Dx	Space step.
character(len=*),	intent(in)		::	BC_L	Left boundary condition type.
character(len=*),	intent(in)		::	BC_R	Right boundary condition type.
real(kind=R_P),	intent(in)		::	initial_state(:,:)	Initial state of primitive variables.
real(kind=R_P),	intent(in)		::	cp0(:)	Initial specific heat, constant pressure.
real(kind=R_P),	intent(in)		::	cv0(:)	Initial specific heat, constant volume.
integer(kind=I_P),	intent(in),	optional	::	steps	Time steps stored.
integer(kind=I_P),	intent(in),	optional	::	ord	Space accuracy formal order.

private pure subroutine reconstruct_interfaces_states(self, primitive, r_primitive)

Reconstruct the interfaces states (into primitive variables formulation) by the requested order of accuracy.

Arguments

Type	Intent		Name
class(euler_1D),	intent(in)	::	self	Euler field.
real(kind=R_P),	intent(in)	::	primitive(1:self%Np,1-self%Ng:self%Ni+self%Ng)	Primitive variables.
real(kind=R_P),	intent(inout)	::	r_primitive(1:self%Np,1:2,0:self%Ni+1)	Reconstructed primitive variables.

private pure subroutine riemann_solver(self, p1, r1, u1, g1, p4, r4, u4, g4, F)

Solve the Riemann problem between the state $1$ and $4$ using the (local) Lax Friedrichs (Rusanov) solver.

Arguments

Type	Intent		Name
class(euler_1D),	intent(in)	::	self	Euler field.
real(kind=R_P),	intent(in)	::	p1	Pressure of state 1.
real(kind=R_P),	intent(in)	::	r1	Density of state 1.
real(kind=R_P),	intent(in)	::	u1	Velocity of state 1.
real(kind=R_P),	intent(in)	::	g1	Specific heats ratio of state 1.
real(kind=R_P),	intent(in)	::	p4	Pressure of state 4.
real(kind=R_P),	intent(in)	::	r4	Density of state 4.
real(kind=R_P),	intent(in)	::	u4	Velocity of state 4.
real(kind=R_P),	intent(in)	::	g4	Specific heats ratio of state 4.
real(kind=R_P),	intent(out)	::	F(1:self%Nc)	Resulting fluxes.

private subroutine update_previous_steps(self, filter, weights)

Update previous time steps.

Arguments

Type	Intent	Optional		Name
class(euler_1D),	intent(inout)		::	self	Euler field.
class(integrand),	intent(in),	optional	::	filter	Filter field displacement.
real(kind=R_P),	intent(in),	optional	::	weights(:)	Weights for filtering the steps.

type_euler_1D Module

Uses:

Used By

Derived Types

type, public, extends(integrand) :: euler_1D

Components

Type-Bound Procedures

Functions

private elemental function E(p, r, u, g) result(energy)

Arguments

Return Value real(kind=R_P)

private elemental function H(p, r, u, g) result(entalpy)

Arguments

Return Value real(kind=R_P)

private elemental function a(p, r, g) result(ss)

Arguments

Return Value real(kind=R_P)

private function add_euler(lhs, rhs) result(opr)

Arguments

Return Value class(integrand), allocatable

private pure function compute_dt(self, Nmax, Tmax, t, CFL) result(Dt)

Arguments

Return Value real(kind=R_P)

private pure function conservative2primitive(self, conservative) result(primitive)

Arguments

Return Value real(kind=R_P) (1:self%Np)

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

Arguments

Return Value class(integrand), allocatable

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

Arguments

Return Value real(kind=R_P)

private function euler_multiply_euler(lhs, rhs) result(opr)

Arguments

Return Value class(integrand), allocatable

private function euler_multiply_real(lhs, rhs) result(opr)

Arguments

Return Value class(integrand), allocatable

private pure function output(self) result(state)

Arguments

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

private elemental function p(r, a, g) result(pressure)

Arguments

Return Value real(kind=R_P)

private function previous_step(self, n) result(previous)

Arguments

Return Value class(integrand), allocatable

private pure function primitive2conservative(self, primitive) result(conservative)

Arguments

Return Value real(kind=R_P) (1:self%Nc)

private elemental function r(p, a, g) result(density)

Arguments

Return Value real(kind=R_P)

private function real_multiply_euler(lhs, rhs) result(opr)

Arguments

Return Value class(integrand), allocatable

private function sub_euler(lhs, rhs) result(opr)

Arguments

Return Value class(integrand), allocatable

Subroutines

private pure subroutine compute_inter_states(r1, p1, u1, g1, r4, p4, u4, g4, p, S, S1, S4)

Arguments

private pure subroutine destroy(self)

Arguments

private subroutine euler_assign_euler(lhs, rhs)

Arguments

private subroutine euler_assign_real(lhs, rhs)

Arguments

private pure subroutine impose_boundary_conditions(self, primitive)

Arguments

private subroutine init(self, Ni, Ns, Dx, BC_L, BC_R, initial_state, cp0, cv0, steps, ord)

Arguments

private pure subroutine reconstruct_interfaces_states(self, primitive, r_primitive)

Arguments

private pure subroutine riemann_solver(self, p1, r1, u1, g1, p4, r4, u4, g4, F)

Arguments

private subroutine update_previous_steps(self, filter, weights)

Arguments