mesh-free lagrangian modelling of fluid dynamics - sintef · mesh-free lagrangian modelling of...

Mesh-free Lagrangian modelling of fluid dynamics

David LE TOUZÉ, Ecole Centrale Nantes

Mesh-free Lagrangian methods in CFD

Smoothed-Particle Hydrodynamics (SPH)

Fast-dynamics free-surface flows

Multi-fluid flows

Fluid-Structure Interactions

HPC: massive interactive simulations

CFD 2011, keynote lecture

David Le Touzé, Ecole Centrale Nantes CFD 2011, keynote lecture

Mesh-free Lagrangian methods

Methods for discrete media Methods for continuous

media

A « particle » is an atom, a

molecule, a grain, etc.

A « particle » is an elementary

mass of considered continuous

medium

Methods directly model laws of

interaction between two

elements

Methods model local PDEs

describing the medium

mechanics/physics

MD, DEM, DSMC… SPH, MPS, FPM, RKPM…

Numerically the discretized local equations

can take the form of a Lagrangian set of

material points (« particles »), implying

intrinsic properties: conservation of linear and

angular momenta, etc.

=> 2 complementary numerical visions:

standard discretized PDEs / particle system


Projection Tesselation Face

reconstruction

True mesh-free

PM… PFEM FVPM SPH, MPS…

Mesh-free Lagrangian methods for fluid dynamics

Mesh-free?


Mesh-free methods, for what purpose?

• to solve situations where meshes have difficulties:

very large deformations of the fluid domain / large motions of multi-bodies

(especially contact between 2 bodies in the flow)

• to avoid costly mesh generating/handling (human cost especially)

Lagrangian methods in fluid, for what purpose?

• to naturally and accurately follow interfaces deformations:

• Complex free surfaces

• Multi-fluid/-phase interfaces

• Fluid-structure interfaces

• to solve fast dynamics flows: no convection term

Lagrangian meshless methods, NOT for what?

• for all problems where mesh-based methods are already reliable (e.g. high-

Re turbulent flows, steady flow, etc.)

Mesh-free Lagrangian methods for fluid dynamics




Multi-fluid flows







1977 : Gingold & Monaghan / Lucy: SPH application field: astrophysics

methodological background: statistics

80’s : mainly applied in astrophysics star formation, self-gravitating clouds, galactic shocks…

then for modeling structures

90’s : astrophysics, structure;

1994: free-surface SPH (Monaghan)

2000’s : astrophysics, structure, fluid dynamics, polymers, surfactants, explosions, lava, porous

media, geotechnical problems, biomechanics, metallurgy…

SPH in fluid dynamics

fast development: SPHERIC ERCOFTAC Special Interest Group:

created in 2005, today: 91 international member entities

a similar method (MPS) is also in fast development in Japan

SPH method: origin


SPH in the world

SPHERIC group : 95 entities of 29 countries worldwide

Annual workshop, benchmarks, bibliography and job databases, codes…


Smoothed Particle Hydrodynamics

Mesh-free Lagrangian

method

Liquids in motion Regularizing

function

A fluid dynamics problem numerically seen as a system of masses

(particles) using a regularizing function.

SPH method: origin


SPH method: characteristics

meshless: no need for handling a mesh

explicit: « easy » and efficient parallelization

Lagrangian: no convective term modeling:

=> accurate for fast dynamics flows (violent impacts, shocks, explosions…)

naturally handles large deformations of the domain:

large motion of (multi-)bodies

arbitrary complex free surface

perfectly non-diffusive interface

permits to include different species (materials, phases…) in a monolithic way

BUT

enhanced versions are needed to get accurate pressure fields

implementation of boundary conditions must be considered with great care

convergence of SPH as usually used is not theoretically proved, heuristically: order 1


SPH method: principle

Lagrangian formalism

equations discretized within a compact zone of influence

differential operators obtained from quantity values at the points included in

this zone of influence

Vi

i j


SPH method: discretization

interpolation

convolution using a kernel W (~test fonction)

interest

estimation of the gradient from the values of the considered quantity

analytical


i j i j i jj

div v v v W x x

i i j j i jj

p p p W x x

D

div vDt

Numerical scheme - inviscid here

=> intrinsic Colagrossi, Antuono,

Le Touzé,

Phys. Rev. E, 2009

Euler equation

Free-surface condition

Initial conditions

Compressible fluid

Dv pg

Dt

, 0 et Dx

p x t v xDt

0 0 0 0, et ,v x t v p x t p

72

0 00

0

17

cP P

SPH discretization: weakly-compressible variant

fully explicit

chosen at the weak-cpr.

limit (Ma=0.1) when

simulating

incompressible flows

= pseudo-compressibility for compatibility (energy conservation)


Stabilization

SPH discretization: weakly-compressible variant

0

0

0

0

0 0

0 0

.

.

ii

v

ii j j i i ij

j Pv

iii j i i i j j j i ij i i

j Pv

d xv

dt

dv v W

dt

dF v F v W S

dt

Method 1

last equations + artificial viscosity added to the pressure term

Method 2

use of a density diffusive term (proportional to a Rusanov flux) in the continuity equation

Method 3

use of an ALE form (Vila, 1999) and of Riemann solvers between each pair of particles

(standard in FVM for compressible flows)

given by the Riemann problem solution


Numerical scheme - viscous here

SPH discretization: incompressible variant

semi-implicit

* 2n n n

i i i iu u u F t

**

i

n

ii turr

*1 11i

i

n ut

p

2

0

*

011

tp i

i

n

or

*

i j ijj

m

1*1

n

ii

n

i pt

uu

2

11

n

i

n

in

i

n

i

uutrr

ISPH_DF ISPH_DI

Pressure Poisson

Equation

0u

21Dup u F

Dt

Solved by standard

incompressible solvers (pre-

conditioned Bi-CGStab…)

Need for correctly imposing

free-surface conditions


fluid

particles

‘ghost’

particles

Solid boundaries handling: ghost particles

principle

solid BCs are imposed thanks to mirrored particles


Exact only for a flat panel, difficulties with geometrical singularities, especially sharp edges

3D generic technique

from any surface (e.g. IGES format)

Solid boundaries handling: ghost particles


Solid boundaries handling: normal flux method

0

0

0

0

0

0 00 .

.

1 1

1 1

.

.

i j j i j ij

j P

i j i j j ij

ii

v

ii j j i i ij

j Pv

iii j i j i ij i i

j P

i

jv i i P

i

d xv

dt

dv v W s v v n W

s F F

dt

dF F W SW

dn

t

x

y

WallFluid domain

h

compensates

missing part of the

kernel support

boundary flux obtained from

compressible flow characteristics

Fully general technique

De Leffe, Le Touzé, Alessandrini, submitted to J. Comput. Phys.


Pressure field quality

Enhanced SPH

Standard SPH

SPH solver: accuracy

Use of density

diffusive term, or

Riemann solver ,or

incompressible

variant…


Accuracy test: gravity wave propagation

SPH solver: accuracy

Standard SPH Enhanced SPH

Additional use of kernel renormalization to get order-1 completeness


The solver SPH-flow

3D

specific tools to enhance model accuracy (Riemann solver, kernel renormalisation…)

variable-size particle algorithm (equivalent to mesh refinment)

generalized ghost technique for modeling any 3D solid boundary

6-dof bodies

efficient parallel model

inflow/outflow conditions implemented

Model core

Extensions of the model

fluid-structure coupling

multifluid flows

Navier-Stokes: viscous flow + turbulence modeling

wave-structure interaction ; shallow-water SPH model ; …

SPH-flow solver

accuracy

HPC

validation

Three key points




Multi-fluid flows







Good prediction of velocity and forces :

Validation on dam breaking test cases

with 80,000 particles only =>

with 1 million particles =>

Fast dynamics free surface flows: validation

Marrone et al., Comput. Meth. Appl. Mech. Eng. 200, 2011

DamBreakVaveFacette2.avi

levelZ.avi


Good prediction of local loads:

Validation on dam breaking test cases

Marrone et al., Comput. Meth. Appl. Mech. Eng. 200, 2011

Fast dynamics free surface flows: validation

../../../../Soutenance_de_these/Kleefsman.avi


24

t (s)

Fz

(N)

0.1 0.2 0.3 0.4

0

100

200

300

400

500

600

Expérience

SPH

Experiment (ECN wave tank)

Vertical force

t (s)

P6

(Pa

)

0.25 0.3 0.35

0

2000

4000 Expérience

SPH

Pressure on the

keel

SPH simulation

3 million particles

6m/s impact

250m long ship at

real scale

Slamming impact

Maruzewski et al., J. Hydraul. Res. 48, 2010

Fast dynamics free surface flows: naval applications

../../../../Présentations/2010/ICHD/MillenFacette1.avi

../../../../Présentations/690/Présentations/2009/IKUS2009/Impact_Cyclope.avi

E:/Présentations/Animations/anim slamming.avi


Violent wave-structure interactions

HOS

SPH Wave

height

on deck


FPSO in severe sea state

coupling strategy:

Fregate facing a dimensioning wave

E:/Présentations/Animations/filmcomparNewHoule2D_3D.avi


t = 0.0625 s t = 0.325 s t = 1.30 s

Experiment in the ECN

tank

SPH calculation

Water height inside the

section

Miship Ro-Ro ferry

section flooding

Other naval applications


Flooding

Fast ship

E:/Présentations/Animations/VedFASTErwanlege.avi


Aquaplanning

tyre

performances

very complex geometry

6 million particles

130 km/h and 50 km/h velocity

1cm-thick layer of water

tyre deformations imposed

Temps adim

Eff

ort

ve

rtic

al(N

)vite

sse

13

0km

/h

Eff

ort

ve

rtic

al(N

)vite

sse

50

km

/h

0

2000

4000

6000

0

20

40

60

Vitesse 130 km/h

Vitesse 50 km/h

Fast dynamics free surface flows: tyre aquaplanning

../../690/Présentations/2009/IKUS2009/Pneu130Facette3.avi

E:/Présentations/Animations/Pneu130Facette3.avi


Aeronautics: aircraft ditching

11° initial trim angle

65 m/s initial velocity

Air effects neglected

3 DOF (X, Z and θ)

6,000,000 particles

Fast dynamics free surface flows: other demonstrative applications

Energy: offshore wind turbines

airbus0_09MC.avi

E:/Présentations/Animations/Airbus_modV.avi

E:/Présentations/Animations/Airbus_modV.avi




Multi-fluid flows







Modification of the standard formulation to preserve density of each phase

Continuous Surface Stress surface tension modelling

Multiphase flow modelling: method 1

Grenier et al., J. Comput. Phys., 2009


In the Riemann-solver ALE formulation, prevent any mass flux through the interface

Multiphase flow modelling: method 2

Leduc et al., Proc. 5th SPHERIC workshop, 2010

i0 i

i ii j , , 0 ij

i i ii j , , , 0 ij E,ij i i

(x )v (x , t)

( )2 v -v (x , t) . 0

( v )2 v v -v (x , t) . g

i

i

E ij E ij i ijj D

E ij E ij E ij i ijj D

d

dt

dW

dt

dp W

dt


Validation on flow past cylinder at Re=200

experiment by Tritton (1959)

Strouhal Cd

SPH 2.0 1.47

Experiment 1.9 1.3

Application of ghost viscous condition only on the pressure gradient term to

preserve the hyperbolicity of the system inviscid part (De Leffe et al., Proc. 6th

SPHERIC workshop, 2011)

2 2.

1

2ij i ji j i ij

i P j P

j i i j

j iP

dEm m W

dtv v

E

p v p v

E

SPH

FVM

Multiphase flow modelling: laminar flow validation

E:/Présentations/Animations/Re_200_wake.avi


Rayleigh-Taylor instabilities

collaboration with CNR-INSEAN (Rome)

Fast convergence on the interface shape

thanks to Lagrangian nature of SPH

Multiphase flow modelling: validations



34

Flooding

experiment

(made in ECN)

comparison

Multiphase flow modelling: validations


Bubbly flows: isolated bubble

Large Bond number

bubble rise

2 = 1

1 = 1000

Level Set (Sussman) SPH



Stokes_SL_AA.avi

E:/Présentations/Animations/Bulle_Sussman_Rho.avi


Bubbly flows: isolated bubble

Small Bond number

bubble rise

Terminal rise velocity

analytic solution

Grenier et al., submitted to J. Multiphase Flows collaboration with CNR-INSEAN (Rome)

E:/Présentations/Animations/Stokes_SL_AA.avi


Bubbly flows: two-merging bubbles

Infinite Bond number and density ratio = 10

SPH SPH

Level-

Set

Level-

Set


Grenier et al., submitted to J. Multiphase Flows

E:/Présentations/Animations/Avi_BubbleMerging/TwoBubbles_Bo_infinity_Curl_LongTimeEvol.avi


Bubbly flows: water-oil separation

Infinite Bond number

Bomin = 0.1

Bomin = 1

naive gravity separator

Grenier et al., submitted to J.

Multiphase Flows


E:/Présentations/Animations/LesBulles_fin.avi

E:/Présentations/Animations/Separateur8.avi




Multi-fluid flows







rigid wedge steel foam resin putty

Fluid-Structure coupling: SPH monolithic coupling

Principle:

each particle has its own continuous medium local equations

mass fluxes through the interface are prevented, as for multiphase method 2


Fluid-Structure coupling: SPH-FEM strategy

Weak coupling strategy, at each substep of Runge-Kutta 4

SPH-FEM coupling

• Imposition of boundary

displacement

• Timestep calculation

• Resolution and time advance

Fluid

• Imposition of boundary

conditions (pressure loading)

• Resolution and time advance

Structure

Pressure load

Boundary

displacement

Timestep of FSI simulations is based on SPH timestep (very small)

In practice, several processors are used to compute flow evolution

while only one is used for solid mechanics

FEM solver is fast and its computation time is masked by the flow

solver => scalabity of SPH-Flow code is unaffected


FEM is an accurate and fast method to simulate structures behaviour under

pressure loads

SPH method easily handles fragmentations and reconnections of free surface

No free-surface tracking method is needed

No specific treatment is needed at the fluid-structure interface

Advantages of SPH-FEM coupling

Fluid-Structure coupling: SPH-FEM strategy

film_Tri_Barrage.avi


SPH-FEM coupling: validation test cases

• Aluminium beam

• High velocity impact

• Motion of the beam is

prescribed at its two ends

Half-wedge hydroelastic impact

Beam deflection at mid point Total vertical force Pressure probe measurements

Fourey et al., submitted to Comput. Meth. Appl. Mech. Engng.

film_Quad_Wedge.avi


Water exit under an

elastic gate experiment

SPH / FEM

Dis

pla

cem

en

t (m

)

Time (s)

displacement of gate end point

x-displacement

y-displacement



film_antoci2.avi

E:/Présentations/Animations/film_antoci2.avi


Total energy evolution for the FSI simulation:

To

tal

en

erg

ies

(S

I)

SPH

FEM

FSI

Water exit under an elastic gate




SPH-FEM coupling: three-dimensional extension

3D water exit under an elastic gate



Tyre deformation when rolling on a wet rough road

SPH-FEM coupling: Example of industrial application

rough road shape

still water

tyre part

collaboration

with Michelin

../../690/Présentations/2009/IKUS2009/Pneu130Facette3.avi




Multi-fluid flows







Initialize

(CAD geometry, no mesh)

Compute

(continuously)

Analyze

(on the fly)

Render

(immersive)

Update

(interactive)

Steer

(interactive)

FP7 European project NextMuSE: SPH & HPC

http://nextmuse.cscs.ch


I

C

A R

U

S

High-performance (HPC) flexible simulation environment

Immersive environment ICARUS:

visualization, analysis, steering of geometry/parameters while

simulation runs on a massively-parallel architecture

Optimization of the method on modern architectures: « manycore » CPUs (MPI/OpenMP) and hybrid GPGPU/CPU

Interactive

ICARUS

robot,

accessible

remotely

O(104) calculation-core simulation

FP7 European project NextMuSE: SPH & HPC

Memory pipe (Distributed Shared Memory buffer)

example of

obtained

scalability

32000

cores

109

calculation

points


Conclusion

Research on mesh-free Lagrangian methods is growing fast and they are

reaching industrial maturity on some problems

These methods can represent a valuable alternative where mesh-based

methods find their limits

They are well suited to:

fast dynamics problems, especially with free-surface

multi-species/multiphase problems with interfaces: multi-fluid, fluid-

structure…

for which they are simple and accurate

These methods could probably be used more in the oil & gas industry

(presently mainly applied to ocean engineering in this industrial field)

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