mus_nonNewtonian_module

This module keeps all information about the nonNewtonian models. Contains routines which calculates non-Newtonian kinematic viscosity according to non-Newtonian model.

It supports three non-Newtonian models: Power law, Carrear Yasuda and Casson. All these models are described in Ashrafizaadeh, M., & Bakhshaei, H. (2009). A comparison of non-Newtonian models for lattice Boltzmann blood flow simulations. Computers and Mathematics with Applications, 58(5), 1045–1054.

For further information about the theory visit the non-newtonian theory page.

Uses

Help

Graph Key

Nodes of different colours represent the following:

Solid arrows point from a submodule to the (sub)module which it is descended from. Dashed arrows point from a module or program unit to modules which it uses.

Used by

Help

Graph Key

Nodes of different colours represent the following:

Solid arrows point from a submodule to the (sub)module which it is descended from. Dashed arrows point from a module or program unit to modules which it uses.

Variables

Type	Visibility	Attributes		Name		Initial
integer,	public,	parameter	::	powerLaw	=	1	Identifier for Power-Law model
integer,	public,	parameter	::	casson	=	2	Identifier for Casson model
integer,	public,	parameter	::	carreauYasuda	=	3	Identifier for Carreau-Yasuda model

Abstract Interfaces

abstract interface

Interface to calculate kinematic viscosity for non-Newtonian model. Viscosity is computed from shear rate which is computed from strain rate which is computed from nonEquilibrium PDF which in turn is computed from pre-collision PDF

private subroutine proc_calc_nNwtn_visc_fromPreColPDF(nNwtn, viscKine, omega, state, neigh, auxField, densPos, velPos, nSize, nSolve, nScalars, nAuxScalars, layout, convFac)

Arguments

Type	Intent		Name
class(mus_nNwtn_type),	intent(in)	::	nNwtn	contains non-Newtonian model parameters loaded from config file
real(kind=rk),	intent(inout)	::	viscKine(:)	output is kinematic viscosity from non-Netonian model
real(kind=rk),	intent(in)	::	omega(:)	Kinematic viscosity omega from last timestep
real(kind=rk),	intent(in)	::	state(:)	state array
integer,	intent(in)	::	neigh(:)	neigh array to obtain precollision pdf
real(kind=rk),	intent(in)	::	auxField(:)	Auxiliary field variable array
integer,	intent(in)	::	densPos	position of density in auxField
integer,	intent(in)	::	velPos(3)	position of velocity components in auxField
integer,	intent(in)	::	nSize	number of elements in state array
integer,	intent(in)	::	nSolve	Number of element to solve in this level
integer,	intent(in)	::	nScalars	number of scalars in state array
integer,	intent(in)	::	nAuxScalars	number of scalars in auxField array
type(mus_scheme_layout_type),	intent(in)	::	layout	scheme layout
type(mus_convertFac_type),	intent(in)	::	convFac	conversion factor to convert lattice to physical units

Derived Types

type, public :: mus_nNwtn_type

The nonNewtonian fluid feature description type

Components

Type	Visibility	Attributes		Name		Initial
logical,	public		::	active	=	.false.	Indicator whether nonNewtonian feature is active maybe not useful. schemeHeader%kind can used to check if nNwtn is active
character(len=labellen),	public		::	label			nonNewtonian fluid model label
integer,	public		::	model			nonNewtonian fluid model identifier
type(mus_nNwtn_PL_type),	public		::	PL			Power Law (PL) model type
type(mus_nNwtn_CY_type),	public		::	CY			Carreau-Yasuda (CY) model type
type(mus_nNwtn_CS_type),	public		::	CS			Casson model type
procedure(proc_calc_nNwtn_visc_fromPreColPDF),	public,	pointer	::	calcVisc	=>	null()	this procedure compute kinematic viscosity in lattice unit on current level from preCollision PDF based on non-Newtonian model. It uses shear-rate to compute viscosity. Non-newtonian model is given in dynamic viscosity in physical unit so it is dimensionalized using viscDyna in physics%fac and lattice kinematic viscosity = lattice dynamic viscosity / rho (local density) for compressible model and lattice kinematic viscosity = lattice dynamic viscosity / rho0 for incompressible model.

type, private :: mus_nNwtn_PL_type

The nonNewtonian power law model parameter

Components

Type	Visibility		Name		Initial
real(kind=rk),	public	::	n	=	0.5_rk	exponentiation parameter
real(kind=rk),	public	::	visc0	=	0.0035_rk	Unit consistency index. Dynamic viscosity parameter when shear rate equals to 1. i.e. backgroud viscosity for power-law model
real(kind=rk),	public	::	nMinus1			parameter for computation

type, private :: mus_nNwtn_CY_type

The nonNewtonian power law model parameter

Components

Type	Visibility		Name		Initial
real(kind=rk),	public	::	n	=	0.2128_rk	model parameter
real(kind=rk),	public	::	a	=	0.64_rk	model parameter
real(kind=rk),	public	::	lambda	=	8.2_rk	model parameter
real(kind=rk),	public	::	visc0	=	0.16_rk	model parameter, dynamic viscosity at zero shear-rate
real(kind=rk),	public	::	viscInf	=	0.0035_rk	model parameter, dynamic viscosity in infinity shear-rate
real(kind=rk),	public	::	nMinus1Div_a	=	(0.2128_rk-1._rk)/0.64_rk	calculated parameter for later usage, nMinus1Div_a = (n-1)/a

type, private :: mus_nNwtn_CS_type

The nonNewtonian power law model parameter

Components

Type	Visibility	Attributes		Name		Initial
real(kind=rk),	public		::	k0	=	0.1937_rk	model parameter
real(kind=rk),	public		::	k1	=	0.055_rk	model parameter

Functions

private function viscPhy_PL(me, shearRate)

nonNewtonian power-law model

Arguments

Type	Intent	Optional	Attributes		Name
type(mus_nNwtn_type),	intent(in)			::	me	nonNewtonian parameters
real(kind=rk),	intent(in)			::	shearRate

Return Value real(kind=rk)

private function viscPhy_CS(me, shearRate)

nonNewtonian Casson model

Arguments

Type	Intent	Optional	Attributes		Name
type(mus_nNwtn_type),	intent(in)			::	me	nonNewtonian parameters
real(kind=rk),	intent(in)			::	shearRate

Return Value real(kind=rk)

private function viscPhy_CY(me, shearRate)

nonNewtonian Carreau-Yasuda model

Arguments

Type	Intent	Optional	Attributes		Name
type(mus_nNwtn_type),	intent(in)			::	me	nonNewtonian parameters
real(kind=rk),	intent(in)			::	shearRate

Return Value real(kind=rk)

Subroutines

public subroutine mus_nNwtn_load(me, conf, parent)

Read in the nonNewtonian table from Lua file and dump parameters to logUnit Specificly, this routine calls each model parameter loader.

Arguments

Type	Intent	Optional		Name
type(mus_nNwtn_type),	intent(out)		::	me	nonNewtonian type
type(flu_State),	intent(inout)		::	conf	lua state
integer,	intent(in),	optional	::	parent	parent handle

public subroutine mus_nNwtn_save2lua(me, conf)

write nonNewtonian fluid parameters into a lua file

Arguments

Type	Intent	Optional	Attributes		Name
type(mus_nNwtn_type),	intent(in)			::	me	nonNewtonian parameters
type(aot_out_type)				::	conf

public subroutine mus_nNwtn_dump2outUnit(me, outUnit)

Dump nonNewtonian fluid parameters to outUnit

Arguments

Type	Intent	Optional	Attributes		Name
type(mus_nNwtn_type),	intent(in)			::	me	nonNewtonian parameters
integer,	intent(in)			::	outUnit

public subroutine mus_assign_nNwtnVisc_ptr(nNwtn, schemeHeader)

This routine assigns function pointer to compute non-Newtonian viscosity

Arguments

Type	Intent	Optional	Attributes		Name
type(mus_nNwtn_type),	intent(inout)			::	nNwtn	non-Newtonian type
type(mus_scheme_header_type),	intent(in)			::	schemeHeader	scheme header

public subroutine calcVisc_CY(nNwtn, viscKine, omega, state, neigh, auxField, densPos, velPos, nSize, nSolve, nScalars, nAuxScalars, layout, convFac)

Calculate kinematic viscosity from nonNewtonian Carreau-Yasuda model. $\mu = \mu_\inf + (\mu_0-\mu_\inf)(1+(\lambdashearRate)a)^((n-1)/a)$

Arguments

Type	Intent		Name
class(mus_nNwtn_type),	intent(in)	::	nNwtn	contains non-Newtonian model parameters loaded from config file
real(kind=rk),	intent(inout)	::	viscKine(:)	output is physical kinematic viscosity will be overwritten by non-Netonian model
real(kind=rk),	intent(in)	::	omega(:)	Kinematic viscosity omega from last timestep
real(kind=rk),	intent(in)	::	state(:)	state array
integer,	intent(in)	::	neigh(:)	neigh array to obtain precollision pdf
real(kind=rk),	intent(in)	::	auxField(:)	Auxiliary field variable array
integer,	intent(in)	::	densPos	position of density in auxField
integer,	intent(in)	::	velPos(3)	position of velocity components in auxField
integer,	intent(in)	::	nSize	number of elements in state array
integer,	intent(in)	::	nSolve	Number of element to solve in this level
integer,	intent(in)	::	nScalars	number of scalars in state array
integer,	intent(in)	::	nAuxScalars	number of scalars in auxField array
type(mus_scheme_layout_type),	intent(in)	::	layout	scheme layout
type(mus_convertFac_type),	intent(in)	::	convFac	conversion factor to convert lattice to physical units

private subroutine mus_nNwtn_PL_load(me, conf, tHandle)

Read in the nonNewtonian Power Law (PL) model parameters from Lua file

Arguments

Type	Intent		Name
type(mus_nNwtn_PL_type),	intent(out)	::	me	nonNewtonian type
type(flu_State),	intent(inout)	::	conf	lua state
integer,	intent(inout)	::	tHandle	nonNewtonian table handle

private subroutine mus_nNwtn_CY_load(me, conf, tHandle)

Read in the nonNewtonian Carreau-Yasuda (CY) model parameters from Lua file

Arguments

Type	Intent		Name
type(mus_nNwtn_CY_type),	intent(out)	::	me	nonNewtonian type
type(flu_State),	intent(inout)	::	conf	lua state
integer,	intent(inout)	::	tHandle	nonNewtonian table handle

private subroutine mus_nNwtn_CS_load(me, conf, tHandle)

Read in the nonNewtonian Casson model parameters from Lua file

Arguments

Type	Intent		Name
type(mus_nNwtn_CS_type),	intent(out)	::	me	nonNewtonian type
type(flu_State),	intent(inout)	::	conf	lua state
integer,	intent(inout)	::	tHandle	nonNewtonian table handle

private subroutine mus_nNwtn_PL_save(me, conf)

write nonNewtonian Power Law (PL) parameters into a lua file

Arguments

Type	Intent	Optional	Attributes		Name
type(mus_nNwtn_PL_type),	intent(in)			::	me	nonNewtonian parameters
type(aot_out_type)				::	conf

private subroutine mus_nNwtn_CY_save(me, conf)

write nonNewtonian (CY) parameters into a lua file

Arguments

Type	Intent	Optional	Attributes		Name
type(mus_nNwtn_CY_type),	intent(in)			::	me	nonNewtonian parameters
type(aot_out_type)				::	conf

private subroutine mus_nNwtn_CS_save(me, conf)

write nonNewtonian Casson parameters into a lua file

Arguments

Type	Intent	Optional	Attributes		Name
type(mus_nNwtn_CS_type),	intent(in)			::	me	nonNewtonian parameters
type(aot_out_type)				::	conf

private subroutine mus_nNwtn_PL_dump(me, outUnit)

Dump nonNewtonian Power Law (PL) parameters to outUnit

Arguments

Type	Intent	Optional	Attributes		Name
type(mus_nNwtn_PL_type),	intent(in)			::	me	nonNewtonian parameters
integer,	intent(in)			::	outUnit

private subroutine mus_nNwtn_CY_dump(me, outUnit)

Dump nonNewtonian (CY) parameters to outUnit

Arguments

Type	Intent	Optional	Attributes		Name
type(mus_nNwtn_CY_type),	intent(in)			::	me	nonNewtonian parameters
integer,	intent(in)			::	outUnit

private subroutine mus_nNwtn_CS_dump(me, outUnit)

Dump nonNewtonian (CY) parameters to outUnit

Arguments

Type	Intent	Optional	Attributes		Name
type(mus_nNwtn_CS_type),	intent(in)			::	me	nonNewtonian parameters
integer,	intent(in)			::	outUnit

private subroutine calcVisc_PL(nNwtn, viscKine, omega, state, neigh, auxField, densPos, velPos, nSize, nSolve, nScalars, nAuxScalars, layout, convFac)

Calculate kinematic viscosity from nonNewtonian power-law model. $\mu = K shearRate^(n-1)$. Shear rate is computed from strain rate which is computed from nonEquilibrium PDF which in turn computed from pre-collision PDF

Arguments

Type	Intent		Name
class(mus_nNwtn_type),	intent(in)	::	nNwtn	contains non-Newtonian model parameters loaded from config file
real(kind=rk),	intent(inout)	::	viscKine(:)	output is physical kinematic viscosity will be overwritten by non-Netonian model
real(kind=rk),	intent(in)	::	omega(:)	Kinematic viscosity omega from last timestep
real(kind=rk),	intent(in)	::	state(:)	state array
integer,	intent(in)	::	neigh(:)	neigh array to obtain precollision pdf
real(kind=rk),	intent(in)	::	auxField(:)	Auxiliary field variable array
integer,	intent(in)	::	densPos	position of density in auxField
integer,	intent(in)	::	velPos(3)	position of velocity components in auxField
integer,	intent(in)	::	nSize	number of elements in state array
integer,	intent(in)	::	nSolve	Number of element to solve in this level
integer,	intent(in)	::	nScalars	number of scalars in state array
integer,	intent(in)	::	nAuxScalars	number of scalars in auxField array
type(mus_scheme_layout_type),	intent(in)	::	layout	scheme layout
type(mus_convertFac_type),	intent(in)	::	convFac	conversion factor to convert lattice to physical units

private subroutine calcVisc_CS(nNwtn, viscKine, omega, state, neigh, auxField, densPos, velPos, nSize, nSolve, nScalars, nAuxScalars, layout, convFac)

Calculate kinematic viscosity from nonNewtonian Casson model. $\mu = (k0 + k1 * sqrt(shearRate))^2/shearRate$

Arguments

Type	Intent		Name
class(mus_nNwtn_type),	intent(in)	::	nNwtn	contains non-Newtonian model parameters loaded from config file
real(kind=rk),	intent(inout)	::	viscKine(:)	output is physical kinematic viscosity will be overwritten by non-Netonian model
real(kind=rk),	intent(in)	::	omega(:)	Kinematic viscosity omega from last timestep
real(kind=rk),	intent(in)	::	state(:)	state array
integer,	intent(in)	::	neigh(:)	neigh array to obtain precollision pdf
real(kind=rk),	intent(in)	::	auxField(:)	Auxiliary field variable array
integer,	intent(in)	::	densPos	position of density in auxField
integer,	intent(in)	::	velPos(3)	position of velocity components in auxField
integer,	intent(in)	::	nSize	number of elements in state array
integer,	intent(in)	::	nSolve	Number of element to solve in this level
integer,	intent(in)	::	nScalars	number of scalars in state array
integer,	intent(in)	::	nAuxScalars	number of scalars in auxField array
type(mus_scheme_layout_type),	intent(in)	::	layout	scheme layout
type(mus_convertFac_type),	intent(in)	::	convFac	conversion factor to convert lattice to physical units

private subroutine calcVisc_incomp_PL(nNwtn, viscKine, omega, state, neigh, auxField, densPos, velPos, nSize, nSolve, nScalars, nAuxScalars, layout, convFac)

Calculate kinematic viscosity from nonNewtonian power-law model for incompressible model $\mu = K shearRate^(n-1)$

Arguments

Type	Intent		Name
class(mus_nNwtn_type),	intent(in)	::	nNwtn	contains non-Newtonian model parameters loaded from config file
real(kind=rk),	intent(inout)	::	viscKine(:)	output is physical kinematic viscosity will be overwritten by non-Netonian model
real(kind=rk),	intent(in)	::	omega(:)	Kinematic viscosity omega from last timestep
real(kind=rk),	intent(in)	::	state(:)	state array
integer,	intent(in)	::	neigh(:)	neigh array to obtain precollision pdf
real(kind=rk),	intent(in)	::	auxField(:)	Auxiliary field variable array
integer,	intent(in)	::	densPos	position of density in auxField
integer,	intent(in)	::	velPos(3)	position of velocity components in auxField
integer,	intent(in)	::	nSize	number of elements in state array
integer,	intent(in)	::	nSolve	Number of element to solve in this level
integer,	intent(in)	::	nScalars	number of scalars in state array
integer,	intent(in)	::	nAuxScalars	number of scalars in auxField array
type(mus_scheme_layout_type),	intent(in)	::	layout	scheme layout
type(mus_convertFac_type),	intent(in)	::	convFac	conversion factor to convert lattice to physical units

private subroutine calcVisc_incomp_CS(nNwtn, viscKine, omega, state, neigh, auxField, densPos, velPos, nSize, nSolve, nScalars, nAuxScalars, layout, convFac)

Calculate kinematic viscosity from nonNewtonian Casson model for incompressible model. $\mu = (k0 + k1 * sqrt(shearRate))^2/shearRate$

Arguments

Type	Intent		Name
class(mus_nNwtn_type),	intent(in)	::	nNwtn	contains non-Newtonian model parameters loaded from config file
real(kind=rk),	intent(inout)	::	viscKine(:)	output is physical kinematic viscosity will be overwritten by non-Netonian model
real(kind=rk),	intent(in)	::	omega(:)	Kinematic viscosity omega from last timestep
real(kind=rk),	intent(in)	::	state(:)	state array
integer,	intent(in)	::	neigh(:)	neigh array to obtain precollision pdf
real(kind=rk),	intent(in)	::	auxField(:)	Auxiliary field variable array
integer,	intent(in)	::	densPos	position of density in auxField
integer,	intent(in)	::	velPos(3)	position of velocity components in auxField
integer,	intent(in)	::	nSize	number of elements in state array
integer,	intent(in)	::	nSolve	Number of element to solve in this level
integer,	intent(in)	::	nScalars	number of scalars in state array
integer,	intent(in)	::	nAuxScalars	number of scalars in auxField array
type(mus_scheme_layout_type),	intent(in)	::	layout	scheme layout
type(mus_convertFac_type),	intent(in)	::	convFac	conversion factor to convert lattice to physical units

private subroutine calcVisc_incomp_CY(nNwtn, viscKine, omega, state, neigh, auxField, densPos, velPos, nSize, nSolve, nScalars, nAuxScalars, layout, convFac)

Calculate kinematic viscosity from nonNewtonian Carreau-Yasuda model for incompressible model. $\mu = \mu_\inf + (\mu_0-\mu_\inf)(1+(\lambdashearRate)a)^((n-1)/a)$

Arguments

Type	Intent		Name
class(mus_nNwtn_type),	intent(in)	::	nNwtn	contains non-Newtonian model parameters loaded from config file
real(kind=rk),	intent(inout)	::	viscKine(:)	output is physical kinematic viscosity will be overwritten by non-Netonian model
real(kind=rk),	intent(in)	::	omega(:)	Kinematic viscosity omega from last timestep
real(kind=rk),	intent(in)	::	state(:)	state array
integer,	intent(in)	::	neigh(:)	neigh array to obtain precollision pdf
real(kind=rk),	intent(in)	::	auxField(:)	Auxiliary field variable array
integer,	intent(in)	::	densPos	position of density in auxField
integer,	intent(in)	::	velPos(3)	position of velocity components in auxField
integer,	intent(in)	::	nSize	number of elements in state array
integer,	intent(in)	::	nSolve	Number of element to solve in this level
integer,	intent(in)	::	nScalars	number of scalars in state array
integer,	intent(in)	::	nAuxScalars	number of scalars in auxField array
type(mus_scheme_layout_type),	intent(in)	::	layout	scheme layout
type(mus_convertFac_type),	intent(in)	::	convFac	conversion factor to convert lattice to physical units

mus_nonNewtonian_module Module

Contents

Variables

Abstract Interfaces

Derived Types

Functions

Subroutines

Uses

Used by

Variables

Abstract Interfaces

abstract interface

private subroutine proc_calc_nNwtn_visc_fromPreColPDF(nNwtn, viscKine, omega, state, neigh, auxField, densPos, velPos, nSize, nSolve, nScalars, nAuxScalars, layout, convFac)

Arguments

Derived Types

type, public :: mus_nNwtn_type

Components

type, private :: mus_nNwtn_PL_type

Components

type, private :: mus_nNwtn_CY_type

Components

type, private :: mus_nNwtn_CS_type

Components

Functions

private function viscPhy_PL(me, shearRate)

Arguments

Return Value real(kind=rk)

private function viscPhy_CS(me, shearRate)

Arguments

Return Value real(kind=rk)

private function viscPhy_CY(me, shearRate)

Arguments

Return Value real(kind=rk)

Subroutines

public subroutine mus_nNwtn_load(me, conf, parent)

Arguments

public subroutine mus_nNwtn_save2lua(me, conf)

Arguments

public subroutine mus_nNwtn_dump2outUnit(me, outUnit)

Arguments

public subroutine mus_assign_nNwtnVisc_ptr(nNwtn, schemeHeader)

Arguments

public subroutine calcVisc_CY(nNwtn, viscKine, omega, state, neigh, auxField, densPos, velPos, nSize, nSolve, nScalars, nAuxScalars, layout, convFac)

Arguments

private subroutine mus_nNwtn_PL_load(me, conf, tHandle)

Arguments

private subroutine mus_nNwtn_CY_load(me, conf, tHandle)

Arguments

private subroutine mus_nNwtn_CS_load(me, conf, tHandle)

Arguments

private subroutine mus_nNwtn_PL_save(me, conf)

Arguments

private subroutine mus_nNwtn_CY_save(me, conf)

Arguments

private subroutine mus_nNwtn_CS_save(me, conf)

Arguments

private subroutine mus_nNwtn_PL_dump(me, outUnit)

Arguments

private subroutine mus_nNwtn_CY_dump(me, outUnit)

Arguments

private subroutine mus_nNwtn_CS_dump(me, outUnit)

Arguments

private subroutine calcVisc_PL(nNwtn, viscKine, omega, state, neigh, auxField, densPos, velPos, nSize, nSolve, nScalars, nAuxScalars, layout, convFac)

Arguments

private subroutine calcVisc_CS(nNwtn, viscKine, omega, state, neigh, auxField, densPos, velPos, nSize, nSolve, nScalars, nAuxScalars, layout, convFac)

Arguments

private subroutine calcVisc_incomp_PL(nNwtn, viscKine, omega, state, neigh, auxField, densPos, velPos, nSize, nSolve, nScalars, nAuxScalars, layout, convFac)

Arguments

private subroutine calcVisc_incomp_CS(nNwtn, viscKine, omega, state, neigh, auxField, densPos, velPos, nSize, nSolve, nScalars, nAuxScalars, layout, convFac)

Arguments

private subroutine calcVisc_incomp_CY(nNwtn, viscKine, omega, state, neigh, auxField, densPos, velPos, nSize, nSolve, nScalars, nAuxScalars, layout, convFac)

Arguments