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Parallel Simulation andParallel Simulation andAnimation of Free Surface FlowAnimation of Free Surface Flow
with the Lattice Boltzmann Methodwith the Lattice Boltzmann Method
Lehrstuhl für Informatik 10 (Systemsimulation)
Universität Erlangen-Nürnberg
www10.informatik.uni-erlangen.de
TUM, July 2006
N. Thürey (LSS Erlangen)
T. Pohl (RRZE Erlangen)
U. Rüde (LSS Erlangen, [email protected])
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Overview
The LBM AlgorithmFree SurfacesApplications
Metal FoamsNano Particles
AdaptivityTime StepsGrid Coarsening
ExtensionsShallow Water CouplingFluid Control
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Overview
The LBM AlgorithmFree SurfacesApplications
Metal FoamsNano Particles
AdaptivityTime StepsGrid Coarsening
ExtensionsShallow Water CouplingFluid Control
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The Lattice-Boltzmann Method (1)The Lattice-Boltzmann Method (1)
Based on cellular automata
Introduced by von Neumann around 1940
Famous: Conway’s Game of Life
Lattice Gas Cellular Automata were used to simulate gases
Complex system with simple rules
Regular grid
Local rules specifying time evolution
Intrinsically parallel for model & simulation, similar to elliptic PDE solvers
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The Lattice-Boltzmann Method (2)The Lattice-Boltzmann Method (2)
Weakly compressible approximation of the Navier-Stokes equations
Easy implementation
Applicable for small Mach numbers (< 0.1)
Easy to adapt, e.g. forComplicated or time-varying geometries
Free surfaces
Additional physical and chemical effects
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The Lattice-Boltzmann Method (3)The Lattice-Boltzmann Method (3)
Real valued representation of particles
Discrete velocities and positions
Algorithm proceeds in two steps:Stream
Collide
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Fluid Cell Treatment
Algorithm proceeds in two steps:•Stream: advect fluid elements (copy DFs to neighbors)•Collide: compute collisions of fluid molecules
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Fluid Cell Treatment
Algorithm proceeds in two steps:•Stream: advect fluid elements (copy DFs to neighbors)•Collide: compute collisions of fluid molecules
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Fluid Cell Treatment
Algorithm proceeds in two steps:•Stream: advect fluid elements (copy DFs to neighbors)•Collide: compute collisions of fluid molecules
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Fluid Cell Treatment
Algorithm proceeds in two steps:•Stream: advect fluid elements (copy DFs to neighbors)•Collide: compute collisions of fluid molecules
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Fluid Cell Treatment
Algorithm proceeds in two steps:•Stream: advect fluid elements (copy DFs to neighbors)•Collide: compute collisions of fluid molecules
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The Collide StepThe Collide Step
Amounts for collisions of particles during movementWeigh equilibrium velocities and velocities from streaming depending on fluid viscosity
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LBM in Equations Stream/Collide:
Equilibrium DF:
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LBM DemonstrationLBM Demonstration(Java applet)
start-applet
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Stability & Turbulence ModellingSmagorinsky Subgrid Model:
Similar to approach for NS-Solvers
Model subgrid-scale vortices by locally changing the viscosity
Implementation for LBMReynolds stress tensor computed for each cell
Changes only in collision operator
Ca. 20% slowdown, significant gain due to decreased resolution requirements
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Falling Drop with Turbulence Model
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Falling Drop with Turbulence Model (slower)
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Overview
The LBM AlgorithmFree SurfacesApplications
Metal FoamsNano Particles
AdaptivityTime StepsGrid Coarsening
ExtensionsShallow Water CouplingFluid Control
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Free surfaces with LBMFree surfaces with LBM
Metal Foams – huge gas volumes
Only simulate and track fluid motion
Compute boundary conditions at free surface
Three cell types: Empty/Gas, Fluid, Interface
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Boundary ConditionsBoundary Conditions
Gas
Liquid
Problem: Missing distribution functions at interface cells after streaming!
Reconstruction such that macroscopic boundary conditions are satisfied.
Körner et al. Lattice Boltzmann Model for Free Surface Flow, Journal of Computational Physics
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Free Surface Treatment
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Free Surface Treatment
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Free Surface Treatment
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Free Surface Treatment
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Free Surface Treatment
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Free Surface Treatment
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Free Surface Treatment
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Free Surface Treatment
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Free surface simulationsFree surface simulations
Algorithmic Overview:
Before stream step, compute mass exchange across cell boundaries for interface cells
Calculate bubble volumes and pressure
Surface curvature for surface tension
Change topology if interface cells become full or empty – keep layer of interface cells closed
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Free Surface Cell Conversions
Emptied interface cell > gasFilled interface cell > fluid
Guarantee closed layer of interface cells
Redistribute mass in the neighborhood
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Curvature calculation (version I)Curvature calculation (version I)
Alternative approaches: Integrate normals over surface (weighted triangles)
Level set methods (track surface as implicit function)
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Surface Tension (Vers. 2)Surface Tension (Vers. 2)
Vδ
ΑΑΑ −=δΑ
Α
1ν_3n
_
2n_
Marching-cube surface triangulationCompute a curvature for each triangle
k=12dAdV
Associate with each LBM cell the average curvature of its trianglesComplicatedBeats level sets for our applications (mass conservation)
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VOF vs. Level-Set MethodsVOF vs. Level-Set Methods
Volume of FluidVolume of Fluid+ Mass + Mass
conservationconservation
+ Efficiency+ Efficiency
+ Good integration + Good integration for LBMfor LBM
Level SetsLevel Sets+ Smooth + Smooth
representationrepresentation
+ Accurate & + Accurate & efficient curvature efficient curvature calculationcalculation
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VisualizationVisualization
Ray-tracing
Refraction
Reflection
Caustics
About 15 Min per frame = 1 day for 4 secs
About same compute time as flow simulation
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Overview
The LBM AlgorithmFree SurfacesApplications
Metal FoamsNano Particles
AdaptivityTime StepsGrid Coarsening
ExtensionsShallow Water CouplingFluid Control
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GlassCeramics
MetalsPolymers
Structural Properties stiffness
energy absorption damping
Functional Properties burner, shock absorber,
heat exchanger, batteries
large, dynamic surface expansion
Examples of FoamsExamples of Foams
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Towards Simulating Metal FoamsTowards Simulating Metal Foams
Bubble growth, Bubble growth, coalescence, collapse, coalescence, collapse, drainage, rheology, etc. are drainage, rheology, etc. are still poorly understoodstill poorly understood
Simulation as a tool to Simulation as a tool to better understand, control better understand, control and optimize the processand optimize the process
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Foaming Simulation 1
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Foaming Simulation 2
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Numerical Experiment: Single Rising BubbleNumerical Experiment: Single Rising Bubble
Validation for Metal Forms or e.g. Bubble Reactors
Comparison to 2D Level-Set Volume of Fluid method and Experimental Results
Modified Parameter: Surface Tension
> External Animation
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Numerical Experiment: Single Rising BubbleNumerical Experiment: Single Rising Bubble
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Parallel PerformanceParallel Performance
LSSLSS-Cluster-Cluster
Fujitsu-SiemensFujitsu-Siemens
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Performance on SR 8000Performance on SR 8000Free surface LBM-Code Free surface LBM-Code
Standard LBM-CodeStandard LBM-Code
Performance lousy on a single node! Conditionals: 2,9 SLBM 51 free surface LBMPentium 4: almost no degradation ~ 10%SR 8000: enormous degradation (pseudo-vector, predictable jumps)
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Overview
The LBM AlgorithmFree SurfacesApplications
Metal FoamsNano Particles
AdaptivityTime StepsGrid Coarsening
ExtensionsShallow Water CouplingFluid Control
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Nanotechnology ApplicationsNanotechnology Applications
Properties of materials and surfaces determined by structure of the nano-scale particles
Possible applications of LBM:Simulate the behavior of particles and particle agglomerates in solutions (e.g. breaking up or further agglomeration)
On a larger scale simulate segregation processes
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Nanotechnology Applications (1)Nanotechnology Applications (1)
Curved Boundaries:Particles are approximates with spheresImprove accuracy of LBM simulations by using curved boundary conditions
Standard No-Slip:Reflect DFs at cell boundary
More accurate:Take distance to boundary surface into account, then interpolate DFs accordingly
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Nanotechnology Nanotechnology ApplicationsApplications
Fluid-Body Interaction:Compute the forces acting upon a body due to the fluid flow around it
Integrate DFs towards the body for all cells on its surface
Body-Fluid Interaction:Bodies moving in the fluid
Modify outgoing DFs at the boundary with the surface velocity of the body
StudienarbeitC. Feichtinger
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Nanotechnology ApplicationsNanotechnology Applications
Moving particle agglomerate in the flow
K. Iglberger - Master Thesis Project
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Overview
The LBM AlgorithmFree SurfacesApplications
Metal FoamsNano Particles
AdaptivityTime StepsGrid Coarsening
ExtensionsShallow Water CouplingFluid Control
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Adaptive Time StepsAdaptive Time Steps
Problems with LBM parametrization:
Gravity driven flows cause strongly varying velocitiesBubble coalescence during foaming processes result in high velocities
Standard LBM Algorithm:Time step size fixed (not a parameter)Grid resolution, velocity, viscosity and time step size are coupled
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Adaptive Time StepsAdaptive Time Steps
Resizing the time step:Only done when the necessity arises (e.g. when high velocities are detected)
Compute the desired time step size, and the corresponding LBM parameters
Rescale the DFs of all fluid cells to match the new parameters
Simulation can be continued with the new time step…
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Overview
The LBM AlgorithmFree SurfacesApplications
Metal FoamsNano Particles
AdaptivityTime StepsGrid Coarsening
ExtensionsShallow Water CouplingFluid Control
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Adaptive Coarsening
Adaptivity:Minimize computations in fluid only regions
Fine grid for free surface, coarse grid for fluid volumes
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Adaptive Coarsening
Adaptivity:Minimize computations in fluid only regions
Fine grid for free surface, coarse grid for fluid volumes
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Grid Transfer
Rescaling of Non-equilibrium DF parts for transferSpatial interpolation necessary
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Grid Transfer
Rescaling of Non-equilibrium DF parts for transferSpatial interpolation necessary
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Grid Transfer
Rescaling of Non-equilibrium DF parts for transferSpatial interpolation necessary
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Grid Transfer
Rescaling of Non-equilibrium DF parts for transferSpatial interpolation necessary
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Grid Transfer
Rescaling of Non-equilibrium DF parts for transferSpatial interpolation necessary
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Adaptive Grids Timestepping
Property of LBM: spatial and temporal resolution coupledLarge resolution means large time steps
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Adaptive Grids Timestepping
Property of LBM: spatial and temporal resolution coupledLarge resolution means large time steps
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Adaptive Grids Timestepping
Property of LBM: spatial and temporal resolution coupledLarge resolution means large time steps
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Adaptive Grids Timestepping
Property of LBM: spatial and temporal resolution coupledLarge resolution means large time steps
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Adaptive Grids Timestepping
Property of LBM: spatial and temporal resolution coupledLarge resolution means large time steps
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Adaptive Grids Timestepping
Property of LBM: spatial and temporal resolution coupledLarge resolution means large time steps
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Adaptive Grids Timestepping
Property of LBM: spatial and temporal resolution coupledLarge resolution means large time steps
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Adaptive Grids Performance
Speed up: factor 2-4 for larger resolutions
Insignifcant overhead for small resolutions
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Overview
The LBM AlgorithmFree SurfacesApplications
Metal FoamsNano Particles
AdaptivityTime StepsGrid Coarsening
ExtensionsShallow Water CouplingFluid Control
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Simulation of Large Scale Open WaterSimulation of Large Scale Open Water
Problem:Huge range of scales: from surface waves to small drops of water
Not resolvable in a single simulation
ApproachSimulate water surface with coupled 2D/3D shallow water / free surface model
Eulerian simulation of drops
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Coupled Shallow Water Simulation
Simulate only a layer on the water surfaceRegion of interest is handled with full 3D simulationWave propagation outside by shallow water model
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Coupled Shallow Water Boundary Conditions
Two layers of boundary conditions
Set height and velocity in outer layer
Set only height in inner layer
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Example Coupled Simulations Example Coupled Simulations
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Overview
The LBM AlgorithmFree SurfacesApplications
Metal FoamsNano Particles
AdaptivityTime StepsGrid Coarsening
ExtensionsShallow Water CouplingFluid Control
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Physically Based AnimationPhysically Based Animation
Special Effects e.g. for Computer generated movies
Realistic appearance necessary, but only where it‘s absolutely necessary
> Control Fluid or other simulations
Examples of Fluid Simulations in Movies: Harry Potter 4 (ship-scene), Ice Age 2 (throughout), Poseidon (in August)
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Detail Preserving Fluid ControlDetail Preserving Fluid Control
Control Fluid without destroying small scale DetailsApply Control Forces only on a large Scale
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Detail Preserving Fluid ControlDetail Preserving Fluid Control
Control Fluid without destroying small scale DetailsApply Control Forces only on a large Scale
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Detail Preserving Fluid ControlDetail Preserving Fluid Control
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Detail Preserving Fluid ControlDetail Preserving Fluid Control
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Detail Preserving Fluid ControlDetail Preserving Fluid Control
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Detail Preserving Fluid ControlDetail Preserving Fluid Control
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Detail Preserving Fluid ControlDetail Preserving Fluid Control
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Simulations with Fluid Control
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Talk is Over
Please wake up!
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The Stream StepThe Stream Step
Move particle distribution functions along corresponding velocity vector
Normalized time step, cell size and particle speed
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Fluid Cell Treatment
Algorithm proceeds in two steps:•Stream: advect fluid elements (copy DFs to neighbors)•Collide: compute collisions of fluid molecules
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Numerical Experiment: Single Rising BubbleNumerical Experiment: Single Rising BubbleUNUSEDUNUSED