group4

Lattice Boltzmann Simulations

with moving objects

Stefan Werner, Maximilian Walther, Jannis Greifenstein

Simulation and Scientific Computing II

Summer Term 2008 Project

21. Juli 2008

S. Werner, M. Walther, J. Greifenstein (LSS)Lattice Boltzmann - Moving objects 21. Juli 2008 1 / 25

Outline

1 Basic concepts

Two model coupling

A short introduction to the Rigid Body Physics Engine

The basic algorithm

2 The algorithm in detail

The flag calculation step

Curved boundary treatment

Force calculations

3 Difficulties and solutions

Visualization

Lubrication

4 Results and Simulations

Outline

1 Basic concepts

Two model coupling

The basic algorithm

Force calculations

Visualization

Lubrication

Outline

1 Basic concepts

Two model coupling

The basic algorithm

Force calculations

Visualization

Lubrication

Outline

1 Basic concepts

Two model coupling

The basic algorithm

Force calculations

Visualization

Lubrication

Basic concepts Two model coupling

Coupling of two independent simulation systems

Basic concepts A short introduction to the Rigid Body Physics Engine

The Rigid Body Physics Engine - Overview

used rigid bodies: spheres, boxes and unions

important functions:

velFromWF(x, y, z)

addForceAtPos(f, x, y, z)

initWorld()

simulationStep(t)

getAABB()

concept of axis-aligned bounding-boxes

velFromWF(x, y, z)

initWorld()

simulationStep(t)

getAABB()

velFromWF(x, y, z)

initWorld()

simulationStep(t)

getAABB()

velFromWF(x, y, z)

initWorld()

simulationStep(t)

getAABB()

velFromWF(x, y, z)

initWorld()

simulationStep(t)

getAABB()

velFromWF(x, y, z)

initWorld()

simulationStep(t)

getAABB()

The pe-BodyReader

Initial status of the rigid bodies is stored in a configuration file

id x // User -specific ID of the box

center <x,y,z> // Global position of the box

lengths <lx,ly ,lz> // Side lengths of the box

material name // Material of the box

// optional parameters :

linear <vx,vy,vz > // Sets the linear velocity of the box

angular <ax,ay ,az> // Sets the angular velocity of the box

translate <dx ,dy,dz> // Translation of the box

rotate <xangle ,yangle ,zangle > // Euler rotation of the box

fixed // Fixes the box ’s position

Basic concepts The basic algorithm

Extensions to the LB algorithm

initialize_lattice ();

initalize_world ();

for (int t = 0; t < timesteps; ++t) {

flag_step ();

collide_step ();

stream_step ();

force_step ();

simulation_step ();

Recall the original LB algorithm:

initialize_lattice ();

for (int t = 0; t < timesteps; ++t) {

collide_step ();

stream_step ();

The algorithm in detail The flag calculation step

Flag calculations

for each cell in the grid {

save old_flag

if (old_flag != NO_SLIP)

set new_flag to initial value (e.g. FLUID ,INFLOW ,...)

for each cell inside a bounding box of a non -fixed object {

if (cell is inside a particle)

set new_flag to OBJECT

// Treatment for state change from OBJECT to FLUID

// be aware of some exceptional cases

if (old_flag == OBJECT && new_flag != OBJECT)

restore the distribution functions with correct density & velocity

How to restore distribution functions

to restore the density take an average value from all neighbouring

cells wich were already fluid in the last step

take the velocity from the nearest surface point of an object

−→ critical issue for mass conservation in the simulation system

The algorithm in detail Curved boundary treatment

curved particle surfaces are only approximated very roughly by the

cubical lattice cells

⇒ calculate exact distance in order to obtain higher accuracy

Delta calculations

take center of fluid cell as start value: (x, y, z)

set delta = 0.0, distance = 1.0

// iterative approximation of the real surface point in direction

// (x_o , y_o , z_o) of the neighbouring object cell

while (iter < max_it && (x, y, z) is no surface point) {

if ((x, y, z) is already inside the object)

distance = - 0.5 * distance

distance = 0.5 * distance;

(x, y, z) += distance * (x_o , y_o , z_o)

delta += distance;

++iter;

The algorithm in detail Force calculations

How to calculate fluid forces acting on objects -

The momentum exchange method

before stream step after stream step

Fobject =∑all xb

18∑α=0

eα[fα(xb) + fα(xf )]

sum only over directions α where the object has a fluid neighbour

|fα(xb) + fα(xf )| is the impulse change for reflected fluid particles,

i.e. distribution functions

Fobject =∑all xb

18∑α=0

Fobject =∑all xb

18∑α=0

Fobject =∑all xb

18∑α=0

Calculation of the reflected distribution functions

Noncritical cells:

fα(xf ) =1

1 + ∆[(1−∆)fα(xf ) + ∆fα(xb) + ∆fα(xf 2) + 6wαρweα · uw ]

Critical cells:

fα(xf ) = fα(xb) + 6wαρweα · uw

Noncritical cells:

fα(xf ) =1

Critical cells:

Noncritical cells:

fα(xf ) =1

Critical cells:

The force step

for each cell inside a bounding box of a non -fixed object {

if( flag == OBJECT ) {

for each direction with FLUID neighbor {

// Calculate the reflected distribution function

calculate delta in order to obtain the exact point on the particle surface

calculate surface velocity with getVelFromWF ()

if ( FLUID cell is noncritical cell )

use standard formula to calculate the reflected distribution functions

else if ( FLUID cell is critical cell )

ignore the calculated delta , take the standard bounce -back condition

// Calculate force from FLUID neighbor on OBJECT cell

apply momentum exchange method to the FLUID -OBJECT pair

add force to the corresponding particle with addForceAtPos ()

Difficulties and solutions Visualization

Visualization - Problems

saving object data in PovRay files is implemented in the pe, but

rendering the simulations takes a lot of time and there are no

functions for visualizing flows

Visualization - Solutions

ParaView can visualize flows very easily but the pe has no vtk-writer

implemented and therefore no objects can be visualized

⇒ implementation of our own vtk-writer for spheres, boxes and unions

setup of the bodies around the origin, after that calculation of

rotation and translation

approximation of the surfaces by triangles and rectangles

Difficulties and solutions Lubrication

First results ...

Adding a lubrication term

if there is only little space between two objects an additional repulsive

force acts on both of them because the fluid film can not move away

fast enough (the so-called lubrication effect)

it can happen that there is no lattice cell between two objects

although in the physics engine is still space in between

⇒ no repulsive force added to the objects

in order to make the behaviour of the objects more realistic, an

additional lubrication force is added to both objects at the end of the

force-step if they are next to each other

if an OBJECT cell is next to another OBJECT cell

lubrication force = 2 * weighting factor in direction of the other OBJECT cell

It works !

Results and Simulations

Comparison between theoretical results and simulation

in order to estimate the accuracy of the simulation, the results are

compared with theoretical predictions

there exists an analytical solution for the drag force acting on a single

sphere in laminar flows (Stokes flow):

FD = 3πν∗d vin ν∗ =2τ − 1

ω− 1)

where ν∗ is the viscosity, d is the diameter of the sphere and vin is the

difference between the fluid and the sphere velocity (all quantities are

lattice quantities here)

ω− 1)

Comparison between theoretical results and simulation (2)

setup: domainsize 1003, inflow,

a single Sphere at (50.0, 50.0, 50.0) with d = 10 lattice cells

Drag Force

calculated simulated Deviation

vin = 0.02

ω = 0.5 1.299933 1.036314 -20.28 %

ω = 1.0 0.433311 0.388293 -10.39 %

ω = 1.5 0.144437 0.156958 8.67 %

vin = 0.08

ω = 0.5 5.199733 4.366672 -16.02 %

ω = 1.0 1.733244 1.914352 10.45 %

ω = 1.5 0.577748 0.897909 55.42 %

Comparison between theoretical results and simulation (2)

setup: domainsize 1003, inflow,

a single Sphere at (50.0, 50.0, 50.0) with d = 10 lattice cells

Drag Force

calculated simulated Deviation

vin = 0.02

ω = 0.5 1.299933 1.036314 -20.28 %

ω = 1.0 0.433311 0.388293 -10.39 %

ω = 1.5 0.144437 0.156958 8.67 %

vin = 0.08

ω = 0.5 5.199733 4.366672 -16.02 %

ω = 1.0 1.733244 1.914352 10.45 %

ω = 1.5 0.577748 0.897909 55.42 %

Mixing still water

Bypassed canal flow

Rotating agglomerate

Some gravity games

Thank you for your attention !

group4

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