Computes analytic quantities. More...

#include <AnalyticQuantities.hpp>

Static Public Member Functions
static FP	meanFreePath (const FP kT, const FP m, const FP timestep)
	Returns the analytical value for the mean free path for a point particle. More...

static FP	kineticContributionsToSRDKinematicShearViscosity (const FP kT, const FP m, const FP meanParticleCountPerCell, const FP srdAngle, const FP timestep)
	Returns the kinetic contributions to the kinematic shear viscosity in SRD. More...

static FP	kineticContributionsToSRDDynamicShearViscosity (const FP kT, const FP m, const FP linearCellSize, const FP meanParticleCountPerCell, const FP srdAngle, const FP timestep)
	Returns the kinetic contributions to the dynamic shear viscosity in SRD. More...

static FP	collisionalContributionsToSRDKinematicShearViscosity (const FP linearCellSize, const FP meanParticleCountPerCell, const FP srdAngle, const FP timestep)
	Returns the collisional contributions to the kinematic shear viscosity in SRD. More...

static FP	collisionalContributionsToSRDDynamicShearViscosity (const FP m, const FP linearCellSize, const FP meanParticleCountPerCell, const FP srdAngle, const FP timestep)
	Returns the collisional contributions to the dynamic shear viscosity in SRD. More...

static FP	SRDKinematicShearViscosity (const FP kT, const FP m, const FP linearCellSize, const FP meanParticleCountPerCell, const FP srdAngle, const FP timestep)
	Returns the kinematic shear viscosity in SRD. More...

static FP	SRDDynamicShearViscosity (const FP kT, const FP m, const FP linearCellSize, const FP meanParticleCountPerCell, const FP srdAngle, const FP timestep)
	Returns the dynamic shear viscosity in SRD. More...

static FP	approximateSelfDiffusionCoefficient (const unsigned int dimensions, const FP kT, const FP m, const FP meanParticleCountPerCell, const FP srdAngle, const FP timestep)
	Returns an approximation for the self-diffusion coefficient $D$. More...

static FP	hydrodynamicRadius (const FP kT, const FP dynamicStressViscosity, const FP selfDiffusionCoefficient)
	Returns the hydrodynamic radius $ R_H $ (Stokes-Einstein radius) of a spherical particle. More...

Detailed Description

Computes analytic quantities.

Definition at line 16 of file AnalyticQuantities.hpp.

Member Function Documentation

◆ approximateSelfDiffusionCoefficient()

FP AnalyticQuantities::approximateSelfDiffusionCoefficient	(	const unsigned int	dimensions,
		const FP	kT,
		const FP	m,
		const FP	meanParticleCountPerCell,
		const FP	srdAngle,
		const FP	timestep
	)

static

Returns an approximation for the self-diffusion coefficient $D$.

As given in Table 1 of "Multi-Particle Collision Dynamics: A Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids" by G. Gompper, T. Ihle, D.M. Kroll, and R.G. Winkler, DOI:10.1007/978-3-540-87706-6_1

Parameters

[in]	dimensions	The spatial dimensions of the system.
[in]	kT	The product of the fluid temperature with Boltzmann's constant.
[in]	m	The fluid particle mass.
[in]	meanParticleCountPerCell	The average number of particles in a simulation cell.
[in]	srdAngle	The angle used in SRD rotations, in radians.
[in]	timestep	The timestep used in the simulation.

Definition at line 88 of file AnalyticQuantities.cpp.

◆ collisionalContributionsToSRDDynamicShearViscosity()

FP AnalyticQuantities::collisionalContributionsToSRDDynamicShearViscosity	(	const FP	m,
		const FP	linearCellSize,
		const FP	meanParticleCountPerCell,
		const FP	srdAngle,
		const FP	timestep
	)

static

Returns the collisional contributions to the dynamic shear viscosity in SRD.

This quantity is often denoted $ \eta^c $. The computed value is based on collisionalContributionsToSRDKinematicShearViscosity.

Parameters

[in]	m	The fluid particle mass.
[in]	linearCellSize	The size of each of the cubic collision cell's edges.
[in]	meanParticleCountPerCell	The mean number of particles per collision cell.
[in]	srdAngle	The angle used in SRD rotations.
[in]	timestep	The timestep used in the simulation.

Definition at line 52 of file AnalyticQuantities.cpp.

◆ collisionalContributionsToSRDKinematicShearViscosity()

FP AnalyticQuantities::collisionalContributionsToSRDKinematicShearViscosity	(	const FP	linearCellSize,
		const FP	meanParticleCountPerCell,
		const FP	srdAngle,
		const FP	timestep
	)

static

Returns the collisional contributions to the kinematic shear viscosity in SRD.

This quantity is often denoted $ \nu^c $. The formula used is given in "Multi-Particle Collision Dynamics: A Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids" by G. Gompper, T. Ihle, D.M. Kroll, and R.G. Winkler, DOI:10.1007/978-3-540-87706-6_1, chapter 4.1.1, formula 39.

Parameters

[in]	linearCellSize	The size of each of the cubic collision cell's edges.
[in]	meanParticleCountPerCell	The mean number of particles per collision cell.
[in]	srdAngle	The angle used in SRD rotations.
[in]	timestep	The timestep used in the simulation.

Definition at line 40 of file AnalyticQuantities.cpp.

◆ hydrodynamicRadius()

FP AnalyticQuantities::hydrodynamicRadius	(	const FP	kT,
		const FP	dynamicStressViscosity,
		const FP	selfDiffusionCoefficient
	)

static

Returns the hydrodynamic radius $ R_H $ (Stokes-Einstein radius) of a spherical particle.

Parameters

[in]	kT	The product of the fluid temperature with Boltzmann's constant.
[in]	dynamicStressViscosity	The dynamic stress viscosity ( $ \eta $ or $ \mu $) of the fluid.
[in]	selfDiffusionCoefficient	The self-diffusion coefficient $D$ of the particle.

Definition at line 99 of file AnalyticQuantities.cpp.

◆ kineticContributionsToSRDDynamicShearViscosity()

FP AnalyticQuantities::kineticContributionsToSRDDynamicShearViscosity	(	const FP	kT,
		const FP	m,
		const FP	linearCellSize,
		const FP	meanParticleCountPerCell,
		const FP	srdAngle,
		const FP	timestep
	)

static

Returns the kinetic contributions to the dynamic shear viscosity in SRD.

This quantity is often denoted $ \eta^k $. The computed value is based on kineticContributionsToSRDKinematicShearViscosity.

Parameters

[in]	kT	The product of the fluid temperature with Boltzmann's constant.
[in]	m	The fluid particle mass.
[in]	linearCellSize	The size of each of the cubic collision cell's edges.
[in]	meanParticleCountPerCell	The mean number of particles per collision cell.
[in]	srdAngle	The angle used in SRD rotations.
[in]	timestep	The timestep used in the simulation.

Definition at line 28 of file AnalyticQuantities.cpp.

◆ kineticContributionsToSRDKinematicShearViscosity()

FP AnalyticQuantities::kineticContributionsToSRDKinematicShearViscosity	(	const FP	kT,
		const FP	m,
		const FP	meanParticleCountPerCell,
		const FP	srdAngle,
		const FP	timestep
	)

static

Returns the kinetic contributions to the kinematic shear viscosity in SRD.

This quantity is often denoted $ \nu^k $. The formula used is given in "Multi-Particle Collision Dynamics: A Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids" by G. Gompper, T. Ihle, D.M. Kroll, and R.G. Winkler, DOI:10.1007/978-3-540-87706-6_1, chapter 4.1.1, formula 32.

Parameters

[in]	kT	The product of the fluid temperature with Boltzmann's constant.
[in]	m	The fluid particle mass.
[in]	meanParticleCountPerCell	The mean number of particles per collision cell.
[in]	srdAngle	The angle used in SRD rotations.
[in]	timestep	The timestep used in the simulation.

Definition at line 15 of file AnalyticQuantities.cpp.

◆ meanFreePath()

FP AnalyticQuantities::meanFreePath	(	const FP	kT,
		const FP	m,
		const FP	timestep
	)

static

Returns the analytical value for the mean free path for a point particle.

Parameters

[in]	kT	The product of the fluid temperature with Boltzmann's constant.
[in]	m	The fluid particle mass.
[in]	timestep	The timestep used in the simulation.

Definition at line 10 of file AnalyticQuantities.cpp.

◆ SRDDynamicShearViscosity()

FP AnalyticQuantities::SRDDynamicShearViscosity	(	const FP	kT,
		const FP	m,
		const FP	linearCellSize,
		const FP	meanParticleCountPerCell,
		const FP	srdAngle,
		const FP	timestep
	)

static

Returns the dynamic shear viscosity in SRD.

This quantity is often denoted $ \eta $. The computed value is the sum of kineticContributionsToSRDDynamicShearViscosity and collisionalContributionsToSRDDynamicShearViscosity.

Parameters

[in]	kT	The product of the fluid temperature with Boltzmann's constant.
[in]	m	The fluid particle mass.
[in]	linearCellSize	The size of each of the cubic collision cell's edges.
[in]	meanParticleCountPerCell	The mean number of particles per collision cell.
[in]	srdAngle	The angle used in SRD rotations.
[in]	timestep	The timestep used in the simulation.

Definition at line 76 of file AnalyticQuantities.cpp.

◆ SRDKinematicShearViscosity()

FP AnalyticQuantities::SRDKinematicShearViscosity	(	const FP	kT,
		const FP	m,
		const FP	linearCellSize,
		const FP	meanParticleCountPerCell,
		const FP	srdAngle,
		const FP	timestep
	)

static

Returns the kinematic shear viscosity in SRD.

This quantity is often denoted $ \nu $. The computed value is the sum of kineticContributionsToSRDKinematicShearViscosity and collisionalContributionsToSRDKinematicShearViscosity

Parameters

[in]	kT	The product of the fluid temperature with Boltzmann's constant.
[in]	m	The fluid particle mass.
[in]	linearCellSize	The size of each of the cubic collision cell's edges.
[in]	meanParticleCountPerCell	The mean number of particles per collision cell.
[in]	srdAngle	The angle used in SRD rotations.
[in]	timestep	The timestep used in the simulation.

Definition at line 64 of file AnalyticQuantities.cpp.

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

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ approximateSelfDiffusionCoefficient()

◆ collisionalContributionsToSRDDynamicShearViscosity()

◆ collisionalContributionsToSRDKinematicShearViscosity()

◆ hydrodynamicRadius()

◆ kineticContributionsToSRDDynamicShearViscosity()

◆ kineticContributionsToSRDKinematicShearViscosity()

◆ meanFreePath()

◆ SRDDynamicShearViscosity()

◆ SRDKinematicShearViscosity()