OneDFSISourceNonLinear - Class for the non-linear source function B of the 1D hyperbolic problem. More...

#include <OneDFSISourceNonLinear.hpp>

Inheritance diagram for OneDFSISourceNonLinear:

Collaboration diagram for OneDFSISourceNonLinear:

Type definitions and Enumerators
typedef OneDFSISource	super

Constructors & Destructor
	OneDFSISourceNonLinear ()
	Empty constructor. More...

	OneDFSISourceNonLinear (const physicsPtr_Type physicsPtr)
	Constructor. More...

virtual	~OneDFSISourceNonLinear ()
	Do nothing destructor. More...

Methods
Real	source (const Real &A, const Real &Q, const ID &row, const UInt &iNode) const
	Evaluate the source term. More...

Real	dSdU (const Real &A, const Real &Q, const ID &row, const ID &column, const UInt &iNode) const
	Evaluate the derivative of the source term. More...

Real	interpolatedNonConservativeSource (const Real &A, const Real &Q, const ID &row, const container2D_Type &bcNodes, const Real &cfl) const
	Evaluate the non-conservative form of the source term at the foot of the outgoing characteristic. More...

Unimplemented Methods
	OneDFSISourceNonLinear (const OneDFSISourceNonLinear &source)

OneDFSISourceNonLinear &	operator= (const OneDFSISourceNonLinear &source)

Additional Inherited Members
Public Types inherited from OneDFSISource
typedef FactorySingleton< Factory< OneDFSISource, OneDFSI::sourceTerm_Type > >	factorySource_Type

typedef OneDFSIPhysics	physics_Type

typedef std::shared_ptr< physics_Type >	physicsPtr_Type

typedef OneDFSIData::container2D_Type	container2D_Type

Public Member Functions inherited from OneDFSISource
	OneDFSISource ()
	Empty constructor. More...

	OneDFSISource (const physicsPtr_Type physicsPtr)
	Constructor. More...

virtual	~OneDFSISource ()
	Do nothing destructor. More...

void	setPhysics (const physicsPtr_Type &physicsPtr)
	Set the physics of the problem. More...

physicsPtr_Type	physics () const
	Get the physics of the problem. More...

Protected Attributes inherited from OneDFSISource
physicsPtr_Type	M_physicsPtr

Detailed Description

OneDFSISourceNonLinear - Class for the non-linear source function B of the 1D hyperbolic problem.

Author: Vincent Martin, Cristiano Malossi

See also: Equations and networks of 1-D models [7]; Geometrical multiscale coupling of 1-D models [12] [13] [3]

The conservative form of the generic hyperbolic problem is

$\frac{\partial \mathbf U}{\partial t} + \frac{\partial \mathbf F(\mathbf U)}{\partial z} + \mathbf S(\mathbf U) = 0,$

where $\mathbf U$ are the conservative variables, $\mathbf F$ the corresponding fluxes, and $\mathbf S$ represents the source terms.

In the present implementation we have:

$\mathbf F(\mathbf U) = \left[\begin{array}{c} Q \\[2ex] \alpha \displaystyle \frac{Q^2}{A} + \displaystyle \displaystyle\int_{0}^A \frac{A}{\rho}\frac{\partial \psi}{\partial A} dA \end{array}\right], \quad \mathbf S(\mathbf U) = \mathbf B(\mathbf U) - \left[\begin{array}{c} 0 \\[2ex] \displaystyle\frac{\partial}{\partial A^0}\displaystyle\int_{0}^A \displaystyle\frac{A}{\rho}\displaystyle\frac{\partial \psi}{\partial A} dA \displaystyle\frac{\partial A^0}{\partial z} + \displaystyle\frac{\partial}{\partial \beta_0}\displaystyle\int_{0}^A \displaystyle\frac{A}{\rho}\displaystyle\frac{\partial \psi}{\partial A} dA \displaystyle\frac{\partial \beta_0}{\partial z} + \displaystyle\frac{\partial}{\partial \beta_1}\displaystyle\int_{0}^A \displaystyle\frac{A}{\rho}\displaystyle\frac{\partial \psi}{\partial A} dA \displaystyle\frac{\partial \beta_1}{\partial z} \end{array}\right]$

where

$\mathbf B(\mathbf U) = \left[\begin{array}{c} 0 \\[2ex] K_r \displaystyle\frac{Q}{A} + \displaystyle\frac{A}{\rho}\left(\displaystyle\frac{\partial \psi}{\partial A^0}\displaystyle\frac{\partial A^0}{\partial z} + \displaystyle\frac{\partial \psi}{\partial \beta_0}\displaystyle\frac{\partial \beta_0}{\partial z} + \displaystyle\frac{\partial \psi}{\partial \beta_1}\displaystyle\frac{\partial \beta_1}{\partial z}\right) + \displaystyle\frac{Q^2}{A}\displaystyle\frac{\partial \alpha}{\partial z} \end{array}\right]$

The assumed wall-law is

$P-P_\mathrm{ext} = \psi(A,A^0,\beta_0, \beta_1, \gamma) = \underbrace{\sqrt{\frac{\pi}{A^0}}\frac{h E}{1-\nu^2}}_{\beta_0} \left(\left(\frac{A}{A^0}\right)^{\beta_1}-1\right) + \underbrace{\frac{T \tan\phi}{4 \sqrt{\pi}}\frac{h E}{1-\nu^2}}_{\displaystyle\gamma} \frac{1}{A\sqrt{A}} \frac{\partial A}{\partial t}.$

This class implements all the interfaces required for the computation of $\mathbf S$ and its derivatives.

Definition at line 108 of file OneDFSISourceNonLinear.hpp.

Member Typedef Documentation

◆ super

typedef OneDFSISource super

Definition at line 115 of file OneDFSISourceNonLinear.hpp.

Constructor & Destructor Documentation

◆ OneDFSISourceNonLinear() [1/3]

OneDFSISourceNonLinear ( )

inlineexplicit

Empty constructor.

Definition at line 124 of file OneDFSISourceNonLinear.hpp.

Here is the caller graph for this function:

◆ OneDFSISourceNonLinear() [2/3]

OneDFSISourceNonLinear ( const physicsPtr_Type physicsPtr )

inlineexplicit

Constructor.

Parameters

physicsPtr pointer to the physics of the problem

Definition at line 130 of file OneDFSISourceNonLinear.hpp.

◆ ~OneDFSISourceNonLinear()

virtual ~OneDFSISourceNonLinear ( )

inlinevirtual

Do nothing destructor.

Definition at line 133 of file OneDFSISourceNonLinear.hpp.

◆ OneDFSISourceNonLinear() [3/3]

OneDFSISourceNonLinear ( const OneDFSISourceNonLinear & source )

explicitprivate

Member Function Documentation

◆ source()

Real source	(	const Real &	A,
		const Real &	Q,
		const ID &	row,
		const UInt &	iNode
	)		const

virtual

Evaluate the source term.

$\begin{array}{rcl} \mathbf S(\mathbf U)_1 & = & 0,\\ \mathbf S(\mathbf U)_2 & = & K_r\displaystyle\frac{Q}{A} -\displaystyle\frac{\beta_0 \beta_1}{\rho(\beta_1+1)} \left(\displaystyle\frac{A}{A^0}\right)^{\beta_1+1}\displaystyle\frac{\partial A^0}{\partial z} + \displaystyle\frac{1}{\rho}\left(\displaystyle\frac{A^0}{(\beta_1+1)} \left(\displaystyle\frac{A}{A^0}\right)^{\beta_1+1}-A\right)\displaystyle\frac{\partial \beta_0}{\partial z}\\[4ex] &+& \displaystyle\frac{A^0 \beta_0}{\rho(\beta_1+1)}\left(\ln\left(\displaystyle\frac{A}{A^0}\right)- \displaystyle\frac{1}{(\beta_1+1)}\right)\left(\displaystyle\frac{A}{A^0}\right)^{\beta_1+1} \displaystyle\frac{\partial \beta_1}{\partial z}+\displaystyle\frac{Q^2}{A}\displaystyle\frac{\partial \alpha}{\partial z}, \end{array}$

Parameters

A	area
Q	flow rate
row	row of the source term
iNode	node of the mesh

Implements OneDFSISource.

Definition at line 50 of file OneDFSISourceNonLinear.cpp.

◆ dSdU()

Real dSdU	(	const Real &	A,
		const Real &	Q,
		const ID &	row,
		const ID &	column,
		const UInt &	iNode
	)		const

virtual

Evaluate the derivative of the source term.

$\displaystyle\frac{\partial \mathbf S}{\partial A} = \left[\begin{array}{c} 0 \\[2ex] -K_r\displaystyle\frac{Q}{A^2}+\displaystyle\frac{1}{\rho}\left(\displaystyle\frac{\partial \psi}{\partial A^0} \displaystyle\frac{\partial A^0}{\partial z} + \displaystyle\frac{\partial \psi}{\partial \beta_0}\displaystyle\frac{\partial \beta_0}{\partial z} + \displaystyle\frac{\partial \psi}{\partial \beta_1}\displaystyle\frac{\partial \beta_1}{\partial z} \right) -\left(\displaystyle\frac{Q}{A}\right)^2\displaystyle\frac{\partial \alpha}{\partial z} \end{array}\right], \quad \displaystyle\frac{\partial \mathbf S}{\partial Q} = \left[\begin{array}{c} 0 \\[2ex] \displaystyle\frac{K_r}{A} + 2 \displaystyle\frac{Q}{A} \displaystyle\frac{\partial \alpha}{\partial z} \end{array}\right].$

Parameters

A	area
Q	flow rate
row	row of the derivative of the source term
column	column of the derivative of the source term
iNode	node of the mesh

Implements OneDFSISource.

Definition at line 84 of file OneDFSISourceNonLinear.cpp.

◆ interpolatedNonConservativeSource()

Real interpolatedNonConservativeSource	(	const Real &	A,
		const Real &	Q,
		const ID &	row,
		const container2D_Type &	bcNodes,
		const Real &	cfl
	)		const

virtual

Evaluate the non-conservative form of the source term at the foot of the outgoing characteristic.

This method is used for imposing the compatibility equations at the boundaries. It interpolates the value between to nodes.

Parameters

A	area
Q	flow rate
row	row of the source term
bcNodes	list of boundary nodes
cfl	cfl used to identify the foot of the characteristic

Implements OneDFSISource.

Definition at line 123 of file OneDFSISourceNonLinear.cpp.

◆ operator=()

OneDFSISourceNonLinear& operator= ( const OneDFSISourceNonLinear & source )

private

The documentation for this class was generated from the following files:

Type definitions and Enumerators

Constructors & Destructor

Methods

Unimplemented Methods

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ super

Constructor & Destructor Documentation

◆ OneDFSISourceNonLinear() [1/3]

◆ OneDFSISourceNonLinear() [2/3]

◆ ~OneDFSISourceNonLinear()

◆ OneDFSISourceNonLinear() [3/3]

Member Function Documentation

◆ source()

◆ dSdU()

◆ interpolatedNonConservativeSource()

◆ operator=()