Interpolation Namespace Reference

Represents the interpolation operations in the MPM. More...

Functions
void	nodalMass (Mesh *mesh, vector< Body * > *bodies)
	Interpolate solid mass from particles to nodes.
void	nodalMassFuid (Mesh *mesh, vector< Body * > *bodies)
	Interpolate fluid mass from particles to nodes.
void	nodalMomentum (Mesh *mesh, vector< Body * > *bodies)
	Interpolate solid momentum from particles to nodes.
void	nodalMomentumFluid (Mesh *mesh, vector< Body * > *bodies)
	Interpolate fluid momentum from particles to nodes.
void	nodalInternalForce (Mesh *mesh, vector< Body * > *bodies)
	Interpolate internal force of solid from particles to nodes.
void	nodalInternalForceFluid (Mesh *mesh, vector< Body * > *bodies)
	Interpolate internal force of fluid from particles to nodes.
void	nodalExternalForce (Mesh *mesh, vector< Body * > *bodies)
	Interpolate external force of solid from particles to nodes.
void	nodalExternalForceFluid (Mesh *mesh, vector< Body * > *bodies)
	Interpolate external force of fluid from particles to nodes.
void	nodalDragForceFluid (Mesh *mesh, vector< Body * > *bodies)
	Interpolate drag force of fluid from particles to nodes.
void	particleStrainIncrement (Mesh *mesh, vector< Body * > *bodies, double time_step)
	Interpolate the strain increment of solid at particle.
void	particleStrainIncrementFluid (Mesh *mesh, vector< Body * > *bodies, double time_step)
	Interpolate the strain increment of fluid at particle.
void	particleVorticityIncrement (Mesh *mesh, vector< Body * > *bodies, double time_step)
	Interpolate vorticity increment of solid at particle.
void	particleDeformationGradient (Mesh *mesh, vector< Body * > *bodies, double time_step)
	Interpolate deformation gradient of solid at particle.
Eigen::Vector3d	interpolateVector (const std::vector< double > &times, const std::vector< Eigen::Vector3d > &values, double itime)

Detailed Description

Represents the interpolation operations in the MPM.

This class allows to interpolate quantities from particles to node and from nodes to particle back.

Function Documentation

interpolateVector()

Eigen::Vector3d Interpolation::interpolateVector	(	const std::vector< double > &	times,
		const std::vector< Eigen::Vector3d > &	values,
		double	itime )

nodalDragForceFluid()

void Interpolation::nodalDragForceFluid	(	Mesh *	mesh,
		vector< Body * > *	bodies )

Interpolate drag force of fluid from particles to nodes.

\( f_{iI}^{drag,f}= \sum_p \frac{m_p^f n g}{k_{ijp}}(v^w_{jp}-v^s_{jp})N_{Ip} \)

At the moment, only the principal values of the hydraulic conductivity in 3D are considered, then:

\( f_{iI}^{drag,f}= \sum_p \frac{m_p^f n g}{k_{ip}}(v^w_{ip}-v^s_{ip})N_{Ip} \)

Parameters

[in]	mesh	Mesh reference
[in]	bodies	A list o Body pointers

nodalExternalForce()

void Interpolation::nodalExternalForce	(	Mesh *	mesh,
		vector< Body * > *	bodies )

Interpolate external force of solid from particles to nodes.

In one phase calculations: \( f_{iI}^{ext} = \sum_p b_{ip} m_p N_{Ip} \)

In two phase calculations: \( f_{iI}^{ext,s} = \sum_p b_{ip} m_p^f N_{Ip} + \sum_p b_{ip} m_p^s N_{Ip} \)

Parameters

[in]	mesh	Mesh reference
[in]	bodies	A list o Body pointers

nodalExternalForceFluid()

void Interpolation::nodalExternalForceFluid	(	Mesh *	mesh,
		vector< Body * > *	bodies )

Interpolate external force of fluid from particles to nodes.

\( f_{iI}^{ext,f}=\sum_p b_{ip} m_p^w N_{Ip} - \sum_p \frac{m_p^f n g}{k_{ijp}}(v^w_{jp}-v^s_{jp})N_{Ip} \)

At the moment, only the principal values of the hydraulic conductivity in 3D are considered, then:

\( f_{iI}^{ext,f}=\sum_p b_{ip} m_p^w N_{Ip} - \sum_p \frac{m_p^f n g}{k_{ip}}(v^w_{ip}-v^s_{ip})N_{Ip} \)

Parameters

[in]	mesh	Mesh reference
[in]	bodies	A list o Body pointers

nodalInternalForce()

void Interpolation::nodalInternalForce	(	Mesh *	mesh,
		vector< Body * > *	bodies )

Interpolate internal force of solid from particles to nodes.

In one phase calculation: \( f_{iI}^{int}=-\sum_p \sigma_{ijp} V_p N_{Ip,i}\)

In two phase calculation: \( f_{iI}^{int,s}=-\sum_p \sigma_{ijp}' N_{Ip,i} V_p + \sum_p p^f N_{Ip,i} V_p\)

Parameters

[in]	mesh	Mesh reference
[in]	bodies	A list o Body pointers

nodalInternalForceFluid()

void Interpolation::nodalInternalForceFluid	(	Mesh *	mesh,
		vector< Body * > *	bodies )

Interpolate internal force of fluid from particles to nodes.

\( f_{iI}^{int,f}= \sum_p n p^f N_{Ip,i} V_p\)

Parameters

[in]	mesh	Mesh reference
[in]	bodies	A list o Body pointers

nodalMass()

void Interpolation::nodalMass	(	Mesh *	mesh,
		vector< Body * > *	bodies )

Interpolate solid mass from particles to nodes.

\( m_I = \sum_p m_p N_{Ip}\)

Parameters

[in]	mesh	Mesh reference
[in]	bodies	A list of Bodies

nodalMassFuid()

void Interpolation::nodalMassFuid	(	Mesh *	mesh,
		vector< Body * > *	bodies )

Interpolate fluid mass from particles to nodes.

\( m_I^f = \sum_p m_p^f N_{Ip}\)

Parameters

[in]	mesh	Mesh reference
[in]	bodies	A list of Bodies

nodalMomentum()

void Interpolation::nodalMomentum	(	Mesh *	mesh,
		vector< Body * > *	bodies )

Interpolate solid momentum from particles to nodes.

\( p_{iI} = \sum_p p_{ip} N_{Ip}\)

Parameters

[in]	mesh	Mesh reference
[in]	bodies	A list o Body pointers

nodalMomentumFluid()

void Interpolation::nodalMomentumFluid	(	Mesh *	mesh,
		vector< Body * > *	bodies )

Interpolate fluid momentum from particles to nodes.

\( p_{iI}^f = \sum_p p_{ip}^f N_{Ip}\)

Parameters

[in]	mesh	Mesh reference
[in]	bodies	A list o Body pointers

particleDeformationGradient()

void Interpolation::particleDeformationGradient	(	Mesh *	mesh,
		vector< Body * > *	bodies,
		double	time_step )

Interpolate deformation gradient of solid at particle.

\( F_{ijp}^{s,n+1} = (\delta_{ik} + \delta t \sum_I N_{Ip,k} v_{iI}^{s,n}) F_{kjp}^{s,n} \)

Parameters

[in]	mesh	Mesh reference
[in]	bodies	A list o Body pointers
[in]	time_step	Time step

particleStrainIncrement()

void Interpolation::particleStrainIncrement	(	Mesh *	mesh,
		vector< Body * > *	bodies,
		double	time_step )

Interpolate the strain increment of solid at particle.

\( \Delta \epsilon_{ijp} = \frac{1}{2}(N_{Ip,j} v_{iI} + N_{Ip,i} v_{jI}) \)

Parameters

[in]	mesh	Mesh reference
[in]	bodies	A list o Body pointers
[in]	time_step	Time step

particleStrainIncrementFluid()

void Interpolation::particleStrainIncrementFluid	(	Mesh *	mesh,
		vector< Body * > *	bodies,
		double	time_step )

Interpolate the strain increment of fluid at particle.

\( \Delta \epsilon_{ijp}^f = \frac{1}{2}(N_{Ip,j} v_{iI}^f + N_{Ip,i} v_{jI}^f) \)

Parameters

[in]	mesh	Mesh reference
[in]	bodies	A list o Body pointers
[in]	time_step	Time step

particleVorticityIncrement()

void Interpolation::particleVorticityIncrement	(	Mesh *	mesh,
		vector< Body * > *	bodies,
		double	time_step )

Interpolate vorticity increment of solid at particle.

\( \Delta \Omega_{ijp} = \frac{1}{2}(N_{Ip,j} v_{iI} - N_{Ip,i} v_{jI}) \)

Parameters

[in]	mesh	Mesh reference
[in]	bodies	A list o Body pointers
[in]	time_step	Time step