simulation of liquid-gas-solid flows with the lattice ...€¦ · simulation of liquid-gas-solid...

Introduction Free Surface LBM Liquid-Gas-Solid Flows Parallel Computing Examples and More References

Simulation of Liquid-Gas-Solid Flows with the LatticeBoltzmann Method

June 21, 2011

Simon Bogner (University Erlangen-Nuremberg)


Fig. Simulation of spherical particles dropped into liquid(http://youtu.be/BWGbqSlQR-M).

Free Surface Flow (i.e., immiscible fluids or liquid-gas flows,respectively)

Particulate Flows (i.e. rigid bodies in the flow)

Extension of existing Lattice Boltzmann approaches into a methodfor liquid-gas-solid flows.

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http://youtu.be/BWGbqSlQR-M



Outline1 Introduction

Lattice Boltzmann Model2 Free Surface LBM

Free Surface Extension3 Liquid-Gas-Solid Flows

Liquid-Solid Flows with LBMLiquid-Gas-Solid Flows with LBM

4 Parallel ComputingWaLBerla and MPIScaling results

5 Examples and MoreExample VideosConclusion

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Table of Contents1 Introduction






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Lattice and discrete velocities

Fig. D3Q19 model

Fig. Stream step

Let us assume the D3Q19model.

We have 19 particle distributionfunctions (PDFs), i.e., fiencodes the fraction of particleswith lattice velocity vi ,(i = 0, .., 18).

The Stream step propagatesPDFs from neighboring cells.

The Collide step does arelaxation of the PDFs in a celltowards a local equilibrium.

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Basic Idea - Interface Tracking

Fig. Different cell types:

gas , liquid , interface ,

and obstacle

The free surface extension is based on(KT04)1 (volume of fluid - approach).Idea: Simulate only the liquid regionand neglect the gas phase.

Track the position of the free surfaceand do lattice Boltzmann inside theliquid region. Therefore different celltypes are needed (see figure).Interface Cells: Cells that have bothgas and liquid in their neighborhood.Form closed boundary between liquidand gas regions.A free surface boundary conditionincorporates the gas pressure.

1Korner, Carolin ; Thies, Michael: Lattice boltzmann model for free surface flow. (2004) 7






and obstacle

The free surface extension is based on(KT04)1 (volume of fluid - approach).Idea: Simulate only the liquid regionand neglect the gas phase.Track the position of the free surfaceand do lattice Boltzmann inside theliquid region. Therefore different celltypes are needed (see figure).

Interface Cells: Cells that have bothgas and liquid in their neighborhood.Form closed boundary between liquidand gas regions.A free surface boundary conditionincorporates the gas pressure.







and obstacle

The free surface extension is based on(KT04)1 (volume of fluid - approach).Idea: Simulate only the liquid regionand neglect the gas phase.Track the position of the free surfaceand do lattice Boltzmann inside theliquid region. Therefore different celltypes are needed (see figure).Interface Cells: Cells that have bothgas and liquid in their neighborhood.

Form closed boundary between liquidand gas regions.A free surface boundary conditionincorporates the gas pressure.







and obstacle

The free surface extension is based on(KT04)1 (volume of fluid - approach).Idea: Simulate only the liquid regionand neglect the gas phase.Track the position of the free surfaceand do lattice Boltzmann inside theliquid region. Therefore different celltypes are needed (see figure).Interface Cells: Cells that have bothgas and liquid in their neighborhood.Form closed boundary between liquidand gas regions.

A free surface boundary conditionincorporates the gas pressure.







and obstacle

The free surface extension is based on(KT04)1 (volume of fluid - approach).Idea: Simulate only the liquid regionand neglect the gas phase.Track the position of the free surfaceand do lattice Boltzmann inside theliquid region. Therefore different celltypes are needed (see figure).Interface Cells: Cells that have bothgas and liquid in their neighborhood.Form closed boundary between liquidand gas regions.A free surface boundary conditionincorporates the gas pressure.




Interface Cells - Fill Levels



and obstacle

Interface cells have a full set of PDFs.

Interface cells have a fill level0 ≤ ϕ ≤ 1, such that

M = ρ · ϕ.

As a result of advection (stream step)the fill level may change (see formulabelow).This mass tracking technique is thefirst step towards a dynamicalboundary.

∆mi (x) =

0, if gas at x + vi

fi (x + vi)− fi (x), if liquid at x + vi

12[ϕ(x) + ϕ(x + vi)][fi (x + vi)− fi (x)], if interface at x + vi.

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and obstacle

Interface cells have a full set of PDFs.Interface cells have a fill level0 ≤ ϕ ≤ 1, such that

M = ρ · ϕ.


∆mi (x) =

0, if gas at x + vi



8






and obstacle


M = ρ · ϕ.

As a result of advection (stream step)the fill level may change (see formulabelow).

This mass tracking technique is thefirst step towards a dynamicalboundary.

∆mi (x) =

0, if gas at x + vi



8






and obstacle


M = ρ · ϕ.


∆mi (x) =

0, if gas at x + vi



8



Interface Cells - Cell Conversion

If ϕ ≤ 0 or ϕ ≥ 1, then the interface cell must be convertedto gas or liquid, respectively.

If such a cell conversion occurs, then cells in the neighborhoodmay have to be converted to interface cells (see figure below).

This assures a closed boundary layer between gas and liquidregions.

Fig. Possible state changes for the interface layer.

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Liquid-Solid Flows with LBM

Moving boundaries induce fluidflow. For a moving no-slip wallone has (Lad)2

f ′i (x, t+δt) = fi (x, t)+

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c2wiρ(x)viuo

Objects are discretized to thelattice by marking the accordingcells as obstacle

Fig. Mapping of a movingobstacle into the lattice.

2Ladd, A.J.C.: Numerical Simulations of Particulate Suspensions via a Discretized Boltzmann Equation Part I

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Momentum Exchange Method

Fluid flow leads to stresses and forces on the boundaries.

A rigid body dynamics engine is then used to calculate theresulting motion of the objects.

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Liquid-Gas-Solid Flows

Problem: Additional cell typethat has to be handleddynamically.

The free surface algorithm relieson the assertion that there is aclosed boundary around theliquid cells.

Fig. Mapping of a movingobstacle into the lattice.

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Liquid-Gas-Solid Flows

Problem: Additional cell typethat has to be handleddynamically.

The free surface algorithm relieson the assertion that there is aclosed boundary around theliquid cells.

Fig. Obstacle to fluid -conversions are critical.

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Complex Cell Conversion Algorithm

Cell conversions from obstacle to fluid (i.e., either liquid,interface or gas) have to conserve the closed layer of interfacecells between gas and liquid (Bog09)3.

For an obstacle cell x that is going to change to a fluid statefor timestep t + δt , let

N := {x + viδt | i ∈ [1..18] and x + viδt is no obstacle cell}be the set of non-obstacle cells in the neighbourhood.

3Bogner, S.: Simulation of Floating Objects in Free-Surface Flow. Diplomarbeit, Jan 2009 14



Complex Cell Conversion Algorithm

Cell conversions from obstacle to fluid (i.e., either liquid,interface or gas) have to conserve the closed layer of interfacecells between gas and liquid (Bog09)3.For an obstacle cell x that is going to change to a fluid statefor timestep t + δt , let

N := {x + viδt | i ∈ [1..18] and x + viδt is no obstacle cell}be the set of non-obstacle cells in the neighbourhood.

3Bogner, S.: Simulation of Floating Objects in Free-Surface Flow. Diplomarbeit, Jan 2009 14



Complex Cell Conversion Algorithm (Cont.)

Correct cell type is determined from local neighborhood N of theconverted cell, i.e.,

If N contains no gas cells: conversion into liquid cell.

The new liquid cell is initialized with an equilibrium set ofPDFs.Therefore local density ρ(x, t + δt) is approximated from Nand u(x, t + δt) = uo is asumed, where uo is the velocity ofthe obstacle.

If N contains both gas and liquid cells: create an interfacecell.

If N contains no liquid cells: conversion into gas cell.

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PDFs are set to equilibrium as for liquid cells.In addition to the PDFs, a fill value has to be interpolatedfrom the neighborhood N.


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WaLBerla Communication Concept

WaLBerla framework: Widely applicable Lattice Boltzmannsoftware framework from Erlangen.

Simulation domain is split into patches, which are thendistributed over the number of processes.Ghostlayer concept.If neighboring patches are residing on different processes, thenthe patch data is communicated via MPI.

Fig. WaLBerla logo, see http://www10.informatik.uni-erlangen.de/Research/Projects/walberla/.

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http://www10.informatik.uni-erlangen.de/Research/Projects/walberla/

http://www10.informatik.uni-erlangen.de/Research/Projects/walberla/



WaLBerla framework: Widely applicable Lattice Boltzmannsoftware framework from Erlangen.Simulation domain is split into patches, which are thendistributed over the number of processes.

Ghostlayer concept.If neighboring patches are residing on different processes, thenthe patch data is communicated via MPI.

17




WaLBerla framework: Widely applicable Lattice Boltzmannsoftware framework from Erlangen.Simulation domain is split into patches, which are thendistributed over the number of processes.Ghostlayer concept.

If neighboring patches are residing on different processes, thenthe patch data is communicated via MPI.

17




WaLBerla framework: Widely applicable Lattice Boltzmannsoftware framework from Erlangen.Simulation domain is split into patches, which are thendistributed over the number of processes.Ghostlayer concept.If neighboring patches are residing on different processes, thenthe patch data is communicated via MPI.

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Ghostlayer with moving obstacles

The information needed for obstacleto fluid conversions fits perfectly intothe ghostlayer concept.

No need for global communication,since only a local neighborhood needsto be considered.

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Scaling Experiment

Particles floating on a free surface (basin partially filled withliquid).

2D - Scaling because of load balancing considerations.

Scaling along X - and Y - axes.

LIMA Cluster, RRZE http://www.rrze.uni-erlangen.de

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http://www.rrze.uni-erlangen.de


Strong Scaling

Fixed problem size: 512× 512× 64 cells, scaling from 16 to256 processes.MLups: Number (M=millions) of lattice cells updated persecond.

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Weak Scaling

Scaling the problem size, from 320× 240× 300 cells on 24processes to: 2560× 1920× 300 cells on 1536 processes.Performance was 998 MLups (i.e., 86% performancecompared to ideal scaling).

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Buoyancy Example

Fig. Buoyancy due to concavity of the object (http://www10.informatik.uni-erlangen.de/gallery3/index.php/movies/3002).

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http://www10.informatik.uni-erlangen.de/gallery3/index.php/movies/3002



Particles Example

Fig. Simulation of spherical particles dropped into liquid(http://youtu.be/BWGbqSlQR-M).

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Rising Bubble in Particulate Flow

Fig. Video of a rising bubble in a particulate flow(http://youtu.be/MTOiDjcVuXU).

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http://youtu.be/MTOiDjcVuXU

http://youtu.be/MTOiDjcVuXU


Conclusion

Method for the simulation of liquid-gas-solid – flows withLattice Boltzmann

Integration into waLBerla with support for high performancecomputers

Future tasks: Improvement and validation of bubble-particleinteraction.

Key application of free surface method: simulation offoaming processes.

Stability of foams is influenced by the presence ofparticles in such a flow.

Possible application: Simulation of foaming and frothflotation processes.

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Thank you very much for listening!

http://www10.informatik.uni-erlangen.de

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http://www10.informatik.uni-erlangen.de

References

[Bog09] Bogner, S.: Simulation of Floating Objects inFree-Surface Flow. Diplomarbeit, Jan 2009

[KT04] Korner, Carolin ; Thies, Michael: Lattice boltzmannmodel for free surface flow. (2004)

[Lad] Ladd, A.J.C.: Numerical Simulations of ParticulateSuspensions via a Discretized Boltzmann Equation Part I.

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