mus_compute_Poisson_module

This module provides the definition and methods to solve poisson equation. author: Kannan Masilamani Implementation is based on: Luo, K., Wu, J., Yi, H., & Tan, H. (2016). International Journal of Heat and Mass Transfer Lattice Boltzmann modelling of electro-thermo-convection in a planar layer of dielectric liquid subjected to unipolar injection and thermal gradient. International Journal of Heat and Mass Transfer, 103, 832–846.

Guo, Z. (2014). A Coupled Lattice Boltzmann Method to Solve Nernst – Planck Model for Simulating Electro-osmotic Flows. Journal of Scientific Computing, (61), 222–238. http://doi.org/10.1007/s10915-014-9820-6

This implementation solve equation of the form $\partial_t \phi = \nabla^2 \phi + G$ $G$ is the source term For Poisson Eq: $G = \frac{\rho_e}{\epsilon_r \epsilon_0}$ For Poisson Boltzmann Linear Eq: $G = -k^2 \phi$ For Poisson Boltzmann nonLinear Eq: $G = \frac{1}{\epsilon_r \epsilon_0} \sum_i { e z_i c_{\infty} N_A exp(-\frac{z e }{k_b T}\phi) }$ For 1:1 Electrolye solution, above equation is simplied to $G = -\frac{-2 c_{\infty} N_A z e}{\epsilon_r \epsilon_0} sinh(\frac{z e }{k_b T}\phi)$

Uses

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Nodes of different colours represent the following:

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Variables

Type	Visibility	Attributes		Name		Initial
integer,	private,	parameter	::	QQ_27	=	27
integer,	private,	parameter	::	QQ_19	=	19
integer,	private,	parameter	::	qN00	=	1
integer,	private,	parameter	::	q0N0	=	2
integer,	private,	parameter	::	q00N	=	3
integer,	private,	parameter	::	q100	=	4
integer,	private,	parameter	::	q010	=	5
integer,	private,	parameter	::	q001	=	6
integer,	private,	parameter	::	q0NN	=	7
integer,	private,	parameter	::	q0N1	=	8
integer,	private,	parameter	::	q01N	=	9
integer,	private,	parameter	::	q011	=	10
integer,	private,	parameter	::	qN0N	=	11
integer,	private,	parameter	::	q10N	=	12
integer,	private,	parameter	::	qN01	=	13
integer,	private,	parameter	::	q101	=	14
integer,	private,	parameter	::	qNN0	=	15
integer,	private,	parameter	::	qN10	=	16
integer,	private,	parameter	::	q1N0	=	17
integer,	private,	parameter	::	q110	=	18
integer,	private,	parameter	::	q000_19	=	19
integer,	private,	parameter	::	qNNN	=	19
integer,	private,	parameter	::	qNN1	=	20
integer,	private,	parameter	::	qN1N	=	21
integer,	private,	parameter	::	qN11	=	22
integer,	private,	parameter	::	q1NN	=	23
integer,	private,	parameter	::	q1N1	=	24
integer,	private,	parameter	::	q11N	=	25
integer,	private,	parameter	::	q111	=	26
integer,	private,	parameter	::	q000_27	=	27
integer,	private,	parameter	::	QQ_9	=	9
integer,	private,	parameter	::	qN0	=	1
integer,	private,	parameter	::	q0N	=	2
integer,	private,	parameter	::	q10	=	3
integer,	private,	parameter	::	q01	=	4
integer,	private,	parameter	::	qNN	=	5
integer,	private,	parameter	::	qN1	=	6
integer,	private,	parameter	::	q1N	=	7
integer,	private,	parameter	::	q11	=	8
integer,	private,	parameter	::	q00_9	=	9

Subroutines

public subroutine mus_Poisson_advRel_d2q9(fieldProp, inState, outState, auxField, neigh, nElems, nSolve, level, layout, params, varSys, derVarPos)

Advection relaxation routine for the poisson equation with an explicit calculation of all equilibrium quantities. Slow and simple. $\nabla^2 \phi = - \frac{\rho_e}{\epsilon_r \epsilon_0}$ The right hand side of equation is added as a source term in mus_apply_sourceTerms routine

Arguments

Type	Intent		Name
type(mus_field_prop_type),	intent(in)	::	fieldProp(:)	Array of field properties (fluid or species)
real(kind=rk),	intent(in)	::	inState(nElems*varSys%nScalars)	input pdf vector
real(kind=rk),	intent(out)	::	outState(nElems*varSys%nScalars)	output pdf vector
real(kind=rk),	intent(inout)	::	auxField(nElems*varSys%nAuxScalars)	Auxiliary field computed from pre-collision state Is updated with correct velocity field for multicomponent models
integer,	intent(in)	::	neigh(nElems*layout%fStencil%QQ)	connectivity vector
integer,	intent(in)	::	nElems	number of elements in state Array
integer,	intent(in)	::	nSolve	number of elements solved in kernel
integer,	intent(in)	::	level	current level
type(mus_scheme_layout_type),	intent(in)	::	layout	current layout
type(mus_param_type),	intent(in)	::	params	global parameters
type(tem_varSys_type),	intent(in)	::	varSys	variable system definition
type(mus_derVarPos_type),	intent(in)	::	derVarPos(:)	position of derived quantities in varsys for all fields

public subroutine mus_Poisson_advRel_generic(fieldProp, inState, outState, auxField, neigh, nElems, nSolve, level, layout, params, varSys, derVarPos)

Arguments

Type	Intent		Name
type(mus_field_prop_type),	intent(in)	::	fieldProp(:)	Array of field properties (fluid or species)
real(kind=rk),	intent(in)	::	inState(nElems*varSys%nScalars)	input pdf vector
real(kind=rk),	intent(out)	::	outState(nElems*varSys%nScalars)	output pdf vector
real(kind=rk),	intent(inout)	::	auxField(nElems*varSys%nAuxScalars)	Auxiliary field computed from pre-collision state Is updated with correct velocity field for multicomponent models
integer,	intent(in)	::	neigh(nElems*layout%fStencil%QQ)	connectivity vector
integer,	intent(in)	::	nElems	number of elements in state Array
integer,	intent(in)	::	nSolve	number of elements solved in kernel
integer,	intent(in)	::	level	current level
type(mus_scheme_layout_type),	intent(in)	::	layout	current layout
type(mus_param_type),	intent(in)	::	params	global parameters
type(tem_varSys_type),	intent(in)	::	varSys	variable system definition
type(mus_derVarPos_type),	intent(in)	::	derVarPos(:)	position of derived quantities in varsys for all fields

public subroutine mus_PBLinear_advRel_generic(fieldProp, inState, outState, auxField, neigh, nElems, nSolve, level, layout, params, varSys, derVarPos)

Advection relaxation routine for the linear poisson boltzmann equation with an explicit calculation of all equilibrium quantities. Slow and simple. $\nabla^2 \phi = k^2 \phi$ Where k^2 is inverse of debye length and in this kernel refered as RHS_coeff $k^2 = \sum_i \frac{ c_{\infty}z_i^2 e^2}{\epsilon_r \epsilon_0 k_b T}$

Arguments

Type	Intent		Name
type(mus_field_prop_type),	intent(in)	::	fieldProp(:)	Array of field properties (fluid or species)
real(kind=rk),	intent(in)	::	inState(nElems*varSys%nScalars)	input pdf vector
real(kind=rk),	intent(out)	::	outState(nElems*varSys%nScalars)	output pdf vector
real(kind=rk),	intent(inout)	::	auxField(nElems*varSys%nAuxScalars)	Auxiliary field computed from pre-collision state Is updated with correct velocity field for multicomponent models
integer,	intent(in)	::	neigh(nElems*layout%fStencil%QQ)	connectivity vector
integer,	intent(in)	::	nElems	number of elements in state Array
integer,	intent(in)	::	nSolve	number of elements solved in kernel
integer,	intent(in)	::	level	current level
type(mus_scheme_layout_type),	intent(in)	::	layout	current layout
type(mus_param_type),	intent(in)	::	params	global parameters
type(tem_varSys_type),	intent(in)	::	varSys	variable system definition
type(mus_derVarPos_type),	intent(in)	::	derVarPos(:)	position of derived quantities in varsys for all fields

public subroutine mus_PBnonLinear_advRel_generic(fieldProp, inState, outState, auxField, neigh, nElems, nSolve, level, layout, params, varSys, derVarPos)

Advection relaxation routine for the nonlinear poisson boltzmann equation for electrolyte solution $\nabla^2 \phi = - \frac{1}{\epsilon_r \epsilon_0} \sum_i { e z_i c_{\infty} N_A exp(-\frac{z e }{k_b T}\phi) }$

Arguments

Type	Intent		Name
type(mus_field_prop_type),	intent(in)	::	fieldProp(:)	Array of field properties (fluid or species)
real(kind=rk),	intent(in)	::	inState(nElems*varSys%nScalars)	input pdf vector
real(kind=rk),	intent(out)	::	outState(nElems*varSys%nScalars)	output pdf vector
real(kind=rk),	intent(inout)	::	auxField(nElems*varSys%nAuxScalars)	Auxiliary field computed from pre-collision state Is updated with correct velocity field for multicomponent models
integer,	intent(in)	::	neigh(nElems*layout%fStencil%QQ)	connectivity vector
integer,	intent(in)	::	nElems	number of elements in state Array
integer,	intent(in)	::	nSolve	number of elements solved in kernel
integer,	intent(in)	::	level	current level
type(mus_scheme_layout_type),	intent(in)	::	layout	current layout
type(mus_param_type),	intent(in)	::	params	global parameters
type(tem_varSys_type),	intent(in)	::	varSys	variable system definition
type(mus_derVarPos_type),	intent(in)	::	derVarPos(:)	position of derived quantities in varsys for all fields

mus_compute_Poisson_module Module

Contents

Variables

Subroutines

Uses

Used by

Variables

Subroutines

public subroutine mus_Poisson_advRel_d2q9(fieldProp, inState, outState, auxField, neigh, nElems, nSolve, level, layout, params, varSys, derVarPos)

Arguments

public subroutine mus_Poisson_advRel_generic(fieldProp, inState, outState, auxField, neigh, nElems, nSolve, level, layout, params, varSys, derVarPos)

Arguments

public subroutine mus_PBLinear_advRel_generic(fieldProp, inState, outState, auxField, neigh, nElems, nSolve, level, layout, params, varSys, derVarPos)

Arguments

public subroutine mus_PBnonLinear_advRel_generic(fieldProp, inState, outState, auxField, neigh, nElems, nSolve, level, layout, params, varSys, derVarPos)

Arguments