D2q9 pf velocity autosym

Description

The 'd2q9_pf_cm' model is a multiphase 2D (planar) lattice Boltzmann model for the simulation of incompressible, immiscible fluids (at both high and low density ratios).

The base implementation uses an incompressible, velocity based LBM for capturing the hydrodynamics of the flow and solves the conservative phase field equation for the interfacial dynamics. To enhance stability, a Multiple-Relaxation-Time and Cascaded collision operator are used.

The MRT model has 2 options at compile time:

• GF: Guo Forcing;

  This is using a higher order Forcing scheme from the work of Guo et al. (2002) for the hydrodynamics

• RT: Ren Temporal

  This is using the Temporal term included in the phase field equilibrium distribution function by Ren et al. (2016)

Publications: " Improved locality of the phase-field lattice Boltzmann model for immiscible fluids at high density ratios " Authors: A. Fakhari, T. Mitchell, C. Leonardi, D. Bolster (2017) DOI: 10.1103/PhysRevE.96.053301

Boundary Conditions options at compile time: * Outflow:

  This is used for outflow boundaries, it is made as an
  option as it requires additional fields for calculations
  so results in a slower code.

• autosym:

  Allows symmetry node type flags introduced in v6.2

Updates: 16/08/2018: Cascaded (CLBM) collision scheme is introduced for both hydrodynamics and phase-field.

Details

Model description files files for this model: Dynamics.c Dynamics.R

Zonal Settings

Name	Comment
PhaseField_init	Initial/Inflow PhaseField distribution
VelocityX	inlet/outlet/init velocity
VelocityY	inlet/outlet/init velocity
Pressure	inlet/outlet/init density
GravitationX	applied (rho)*GravitationX
GravitationY	applied (rho)*GravitationY
PressureLossInObj	Weight of [pressure loss] in objective
OutletFluxInObj	Weight of [pressure loss] in objective
InletFluxInObj	Weight of [pressure loss] in objective
TotalDensityInObj	Weight of [Mass conservation check] in objective
RTIBubbleInObj	Weight of [Bubble Tracker] in objective
RTISpikeInObj	Weight of [Spike Tracker] in objective
NMovingWallForceInObj	Weight of [force exerted on the N Moving Wall] in objective
NMovingWallPowerInObj	Weight of [implented: Vx* incoming momentum (precollision)] in objective
FDragInObj	Weight of [Force exerted on body in X-direction] in objective
FLiftInObj	Weight of [Force exerted on body in Y-direction] in objective
FTotalInObj	Weight of [Force exerted on body in X+Y -direction] in objective

Global Settings

Name	Derived	Comment
Period		Number of cells per cos wave
Perturbation		Size of wave perturbation, Perturbation Period
MidPoint		height of RTI centerline
Radius		Radius of diffuse interface circle
CenterX		Circle center x-coord
CenterY		Circle Center y-coord
BubbleType		Drop/bubble
Density_h		High density fluid
Density_l		Low density fluid
PhaseField_h		PhaseField in high density fluid
PhaseField_l		PhaseField in low density fluid
W		Anti-diffusivity coeff (phase interfacial thickness)
omega_phi	1.0/(3*M+0.5)	one over relaxation time (phase field)
M		Mobility
sigma		surface tension
ContactAngle		Contact angle in degrees - in reference to the high density fluid
radAngle	ContactAngle*3.1415926535897/180	Conversion to rads for calcs
tau_l	(3*Viscosity_l)	relaxation time (low density fluid)
tau_h	(3*Viscosity_h)	relaxation time (high density fluid)
Viscosity_l		kinematic viscosity
Viscosity_h		kinematic viscosity
omega_bulk	1.0/(3*bulk_visc+0.5)	inverse of bulk relaxation time
bulk_visc		bulk viscosity
BuoyancyX		applied (rho-rho_h)*BuoyancyX
BuoyancyY		applied (rho-rho_h)*BuoyancyY
fixedIterator		fixed iterator for velocity calculation
Threshold		Parameters threshold

Exported Quantities (VTK, etc)

Name	Unit	Comment
Rho	kg/m3	Rho
PhaseField	1	PhaseField
U	m/s	U
NormalizedPressure	Pa	NormalizedPressure
Pressure	Pa	Pressure
Normal	1	Normal

Exported Global Integrals (CSV, etc)

Name	Unit	Comment
RTIBubble	1	Bubble Tracker
RTISpike	1	Spike Tracker
PressureLoss	1mPa	pressure loss
OutletFlux	1m2/s	pressure loss
InletFlux	1m2/s	pressure loss
TotalDensity	1kg/m3	Mass conservation check
NMovingWallForce	1	force exerted on the N Moving Wall
NMovingWallPower	1	implented: Vx* incoming momentum (precollision)
FDrag	N	Force exerted on body in X-direction
FLift	N	Force exerted on body in Y-direction
FTotal	N	Force exerted on body in X+Y -direction
Objective	1	Objective function

Node Types

Group	Types
ADDITIONALS	SpikeTrack, BubbleTrack, Smoothing
BODY	Body
BOUNDARY	MovingWall_N, MovingWall_S, NVelocity, WVelocity, Solid, Wall
COLLISION	BGK, MRT
SETTINGZONE	DefaultZone
SYMX	SymmetryX_plus, SymmetryX_minus
SYMY	SymmetryY_plus, SymmetryY_minus

Solved fields

Name	Access pattern	Comment
g[0]		g[0]
g[1]		g[1]
g[2]		g[2]
g[3]		g[3]
g[4]		g[4]
g[5]		g[5]
g[6]		g[6]
g[7]		g[7]
g[8]		g[8]
h[0]		h[0]
h[1]		h[1]
h[2]		h[2]
h[3]		h[3]
h[4]		h[4]
h[5]		h[5]
h[6]		h[6]
h[7]		h[7]
h[8]		h[8]
nw_x		phase field normal at the wall in x direction, pointing into fluid
nw_y		nw_y
U		U
V		V
PhaseF		PhaseF

Densities - default accessors

Name	Field	Pulling field from	Comment
g[0]	g[0]		g[0]
g[1]	g[1]		g[1]
g[2]	g[2]		g[2]
g[3]	g[3]		g[3]
g[4]	g[4]		g[4]
g[5]	g[5]		g[5]
g[6]	g[6]		g[6]
g[7]	g[7]		g[7]
g[8]	g[8]		g[8]
h[0]	h[0]		h[0]
h[1]	h[1]		h[1]
h[2]	h[2]		h[2]
h[3]	h[3]		h[3]
h[4]	h[4]		h[4]
h[5]	h[5]		h[5]
h[6]	h[6]		h[6]
h[7]	h[7]		h[7]
h[8]	h[8]		h[8]
nw_x	nw_x		phase field normal at the wall in x direction, pointing into fluid
nw_y	nw_y		nw_y
U	U		U
V	V		V

Action stages

Name	Main procedure	Preloaded densities	Pushed fields
PhaseInit	Init_phase	none	PhaseF
WallInit	Init_wallNorm	none	nw_x, nw_y
BaseInit	Init_distributions	none	g[0], g[1], g[2], g[3], g[4], g[5], g[6], g[7], g[8], h[0], h[1], h[2], h[3], h[4], h[5], h[6], h[7], h[8], U, V
BaseIter	calcHydroIter	g[0], g[1], g[2], g[3], g[4], g[5], g[6], g[7], g[8], h[0], h[1], h[2], h[3], h[4], h[5], h[6], h[7], h[8], nw_x, nw_y, U, V	g[0], g[1], g[2], g[3], g[4], g[5], g[6], g[7], g[8], h[0], h[1], h[2], h[3], h[4], h[5], h[6], h[7], h[8], nw_x, nw_y, U, V
PhaseIter	calcPhaseFIter	g[0], g[1], g[2], g[3], g[4], g[5], g[6], g[7], g[8], h[0], h[1], h[2], h[3], h[4], h[5], h[6], h[7], h[8], nw_x, nw_y, U, V	PhaseF
WallIter	calcWallPhaseIter	nw_x, nw_y	PhaseF

Actions

Name	Stages
Iteration	BaseIter, PhaseIter, WallIter
Init	PhaseInit, WallInit, WallIter, BaseInit