Smoothed Particle Hydrodynamics - Methodology and … · 2019-11-06 · M. B. Liu (刘谋斌) [email protected] . November 30, 2016 @NTU. Recent Progress on meshless methods for Flow

M. B. Liu (刘谋斌)

[email protected]

November 30, 2016

@NTU

Recent Progress on meshless methods for Flow Simulations—SPH, MPS, DPD

Smoothed Particle Hydrodynamics - Methodology and Applications

MES, Peking University—History

Peiyuan Zhou

• 1952—Established by Peiyuan Zhou at Peking University, 1st Dept. Mech. in PRC

• 1958—China’s first low-speed wind tunnel

• 2000—State Key Laboratory for Turbulence and Complex Systems

• 2006—Joined in COE

• 2012— Ranked as NO.1 in PRC

• 450 faculty, 3200 B.S., 820 M.S., 280 Ph.D.

60th Anniversary Celebration

The MES serves the world by providing a high-quality learning

environment, outstanding research laboratories, and challenging

experiences for our students in science, industry and technology.

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MES, Peking University—Divisions

Fluid Mechanics •Turbulence

•Computational fluid dynamics methods

•Aerodynamics

•Propulsion, heat transfer and advanced engines

Solid Mechanics •Micro/nano-mechanics, mechanics and physics of

complex materials

•Mechanics of smart materials and structures

•Elasticity and plasticity

•Experimental mechanics

Engineering Mechanics •Computational mechanics,

•Fluid-structure interaction

•Mesh and meshfree methods

•Structural dynamics

•Mesh generation

Biomechanics and Medical Engineering •Cell mechanics •Bio-solid mechanics •Bio-fluid mechanics •Mechanobiology •Bio-imaging and bio-instrumentation

Dynamics and Control •Cooperative control of multi-agent systems

•Robust tracking control

•Redundant control and dynamic control allocation

•Nonlinear dynamics and control

•Dynamics and control of systems with group symmetries

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Research team – Computational FSI

Impact and penetration

LNG船液舱

液面变形、破碎

结构变形、破坏

强流固耦合作用

Liquid sloshing

网格类，FVM…

粒子类，SPH…

耦合类，SPH/FEM

Numerical methods Key issues

CPU,GPU,CPU+GPU

高性能计算技术复杂载荷作用下的流体运动规律、流固耦合效应、结构失稳与破坏及防护

Computational Mechanics, FSI, Multi-scale modeling

底板

焊板

Explosive welding

Powder Transport Gas-particle two-

phase flow

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Outline

Background

SPH methodology

SPH for hydrodynamics

SPH for environmental flows

SPH for explosion and impact

Prospects and future directions

1

2

3

4

5

6

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1. Background

Explosion and impact Water discharge and dam collapse with free surface

Tsunami with complex interface dynamics

1.1 Continuum scale complex problems Examples: tsunami, dam collapse, penetration…

Difficulties:

Free surfaces, deformable boundaries, moving interfaces (for FDM)

Large deformations (for FEM)

Complex mesh generation and mesh adaptivity (for both FDM and FEM)

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Lagrangian grid-based methods

Eulerian grid-based method

Grid moving with object

Easy to get time history of movement and deformation

Convenient to track moving features

Difficult to treat large deformations

Grid fixed on space

Easy to treat large deformations

Difficult to get time history

Difficult to track moving features

Particle methods such as SPH combine

advantages of FDM & FEM

1. Background Difficulties for FDM/FEM

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1. Background

It is a great challenge to generate or adapt mesh: structured/unstructured, body-fitting, mesh adaptivity, moving mesh, mesh rezoning…, Cost 2/3 work load

Mesh adaptivity

Moving mesh Mesh rezoning

Meshing problems

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1. Background

Landslide and mud flow

Discontinuous problems Granular flows in environmental, chemical, geophysical, bio-engineering…

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1. Background 1.2 Micro/Nano scale problems Traditional numerical methods based on continuum scale

constitutive equations may not be valid, especially when the dimension diminishes…

1.3 Problems with multi-scale physics Coupling MD with FDM/FEM is complicated and not natural…

Evolution of a polymer drop break-up

Cross section of a bilayer of lipid in water molecules

Water droplets in oil

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1. Background

http://www.worldscientific.com/worldscibooks/10.1142/9017

http://www.worldscientific.com/worldscibooks/10.1142/5430

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2. SPH methodology – Basic concepts

2.1 History Originally invented for solving astrophysical problems in open space

Recently applied to general fluid dynamic problems

2.2 Numerical approximation Weight function (or smoothing function ) , W, centered on particles

and describe continuous or discrete field function,

Kernel approximation:

Particle approximation:

( ) ( )i if f W d x x x

1

N

i j ij j j

j

f f W m

, ,( )i if f W d x x

, ,

1

N

i j i j j

j

f f W m

i

j

rij Rcut

SW

SPH approximations in a two-dimensional space

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Liu & Liu, WSPC, 2003; 2015

2.3 SPH equations of motion

N

j

ijji Wm

1

N

j

ij

ji

Wm

Dt

D

1

)(

i

jix

v-v

N

j i

ij

ji

jjii

j

i

ijN

j ji

ji

j

Wm

Wppm

Dt

D

11

xx

v i

i

ijN

j j

jj

i

iij

i

ijN

j j

j

i

ij

Wm

Wppm

Dt

D

xx

v i

122

122

)()(

)3

2(

111

ijiji

N

j j

jij

ji

N

j j

jij

ji

N

j j

j

i WmWmWm

vx

vx

v

ii

ii

i

iN

j

ij

ji

ji

ji

Wppm

Dt

De

2)(

2

1

1

i

jix

v-v

ii

i

iN

j

ij

j

j

i

ij

iWpp

mDt

De

2))((

2

1

122

i

jix

v-v

Density

Momentum

Energy

Strain rate

2. SPH methodology – Basic concepts 13/68

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2. SPH methodology – Basic concepts

2.4 Features and advantages

Features

• Particles are used to represent the state of a system

• Governing equations are discretized and approximated on particles

• Particles move with the object

Merits/demerits

• Mass rigorously conserved, no loss/gain

• Easy to treat large deformations

• Easy to obtain time history of movement and deformations

• Method under development

• Heavier computational cost

Particle method

Meshfree method

Lagrangian method

SPH combines advantages of FDM &

FEM

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2.5 Constructing smoothing function

2. SPH methodology – Improvements

Original SPH empirically specifies that the weight function W satisfies some special requirements like (a) normalization , (b) Delta function property , and (c) symmetric (even) property.

Weight function constructing conditions

( , ) 1W h d

x x x

0lim ( , ) ( )h

W h

x x x x

( )

1

0

( )( ) ( , ) ( )

!( )

jnj

n

j

fW h df r

j

x

x x x x x x xx

2

0

1

2

( , ) 1

( ) ( , ) 0

( ) ( , ) 0

( ) ( , ) 0n

n

W h d

W h d

W h d

W

M

M

h d

M

M

x x x

x x x x x

x x x x x

x x x x x

( )

1

0

( 1) ( )( ) ( ) ( )

!

n j jj

n

j

ff r

j

xx x x x x

Taylor series analysis ( ) () , )( Wf h df

x x xxx

Example: a quartic weight function

20 1 2( , ) ,n

nW h a a R a R a R Rh

x xx x

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Liu et al., JCAM, 2003

2.6 Improving accuracy - FPM


The original SPH method does not have C0 consistency for particle approximation, so the numerical accuracy of the original SPH method is quite low especially for disordered particles or boundary particles.

Finite particle method (FPM), retaining the advantages of SPH with higher order accuracy .

FPM has C0 and C1 consistency for particle approximation.

FPM is not influenced by disordered particle distribution and the selection of smoothing function.

FPM is more computational expensive than the original SPH.

1

1 1 1

,

, , ,

1 1 1

( )

( )

j i

j i

N N N

ij j ij j j ij j

j j ji

N N Ni

ij j ij j j ij j

j j j

W v W v f W vf

fW v W v f W v

x x

x x

Numerical scheme of FPM

Original SPH particle approximation 1

N

i j ij j j

j

f f W m

, ,

1

N

i j i j j

j

f f W m

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Liu et al., AMM, 2005; ANM, 2006.

0 0.5 1 1.5 2 2.5 3 3.5

x 10-5

0

0.2

0.4

0.6

0.8

1x 10

-3

velocity (m/s)

z (

m)

Analytical solutions

SPH results

0.01 s 0.1 s

1 s

Accuracy and stability of SPH and FPM

0 0.5 1 1.5 2 2.5

x 10-5

0

0.2

0.4

0.6

0.8

1x 10

-3

velocity (m/s)

z (m

)

FPM results

Analytical solutions

0.01 s

0.1 s 1 s

Conventional SPH

Improved scheme (FPM) numerical

oscillation removed

1

N

i j ij j j

j

f f W m

, ,

1

N

i j i j j

j

f f W m

1

1 1 1

,

, , ,

1 1 1

( )

( )

j i

j i

N N N

ij j ij j j ij j

j j ji

N N Ni

ij j ij j j ij j

j j j

W v W v f W vf

fW v W v f W v

x x

x x

2.6 Improving accuracy - FPM

2. SPH methodology – Improvements 17/68

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2.7 Adapting SPH (ASPH)


W

i

j

rij

h

S W

i

j

S

rij h

1h

2

SPH: isotropic weight function

ASPH: anisotropic weight function different axes to match the particle spacing as it varies in time, space and direction Capable of catching anisotropic deformation suitable for problems with large dimension ratio

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Liu et al., JSW, 2006

SPH: flow in a micro channel with 800 particles

SPH: a metal bar impacting on a solid wall

2.7 Adapting SPH (ASPH)

ASPH: flow in a micro channel with 200 particles

ASPH: a metal bar impacting on a solid wall

2. SPH methodology – Improvements 19/68

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Liu et al., JSW, 2006

2.8 Solid boundary treatment (SBT)


As a meshfree, Lagrangian particle method, SPH is difficult in exactly implementing solid boundary conditions (SBC).

Virtual particles are usually used to implicitly implement SBC, and the distribution of virtual particles and the calculation of their properties influence the accuracy of SPH simulation.

A new SBT algorithm—coupled dynamic SBT：

1、Two types of virtual particles：Repulsive and ghost particles

2、New repulsive force and new approximation scheme

/(0.75 )ij ijr h

2

2

2 / 3 0 2 / 3

(2 1.5 ) 2 / 3 1( )

0.5(2 ) 1 2

0

f

otherwise

2

20.01 ( )

ij

ij

ij

c fr

x

F

1 0 1.51.5

ij

ij

rr d

d

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Liu et al., JHD, 2013

2.8 Solid boundary treatment (SBT)


Conventional SBT algorithms in SPH lead to pressure oscillation, and large errors in calculating pressure load on structures

The new SBT algorithm produces smooth and accurate pressure field and is more attractive for FSI problems.

A typical example: dam collapse

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3. SPH for hydrodynamics – Free surface flows

Liu M. B. et al., ArCME, 2010

With fixed, moving or deformable boundaries • Dam collapse and water discharge

• Tsunami and flooding

• Wave dynamics

• Liquid drop dynamics

• …

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Dam collapse

Shao, Liu et al., IJCM, 2010

Water discharge

3.1 Dam collapse and water discharge

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3.2 Water impact – dam break against an obstacle

Liu & Shao, SCPMA, 2012

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3.2 Wave impact – water impact on building

Without mitigation

Mitigation with a dike

Top-bottom view

Front-back view

Initial particle distribution

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3.3 Injection flow

Water injection into an empty container

Water injection into a filled container

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3.3 Water injection

Experiment SPH simulation

Water injection

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3.4 Multi-phase flows – liquid drop impact on thin liquid film

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Ma, Liu et al., APS, 2012


3.4 Multi-phase flows – Rayleigh-Taylor instability

Heavier fluid: 1800 kg/m3 Lighter fluid: 1000 kg/m3

Present HU et al. 2007

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Chen, Liu* et al., JCP, 2013


3.4 Multi-phase flows – Air bubble rising

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Chen, Liu* et al., JCP, 2013

3. SPH for hydrodynamics – FSI problems

3.5 Water entry – cylinder

Liu and Shao, ICCEES, 2011

Penetration depth

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3.5 Water entry – wedge

Falling velocity

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Liu et al., IJNMF, 2014


3.6 Water exit – cylinder

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Liu et al., IJNMF, 2014


3.6 Water exit – Projectile launch

Projectile launch directly from water

Projectile launch from a canister

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3.6 Water exit – Projectile launch

The Principle of Independence of the Cavity Sections Expansion

Vlandimir et al., artificial supercavitation, 2002.

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3.7 Liquid sloshing

Water sloshing in a reservoir

LNG船液舱

Liquid fuel sloshing in aerospace and aeronautical vehicles。

LNG sloshing in a LNG ship

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3.7 Liquid sloshing – in a rectangular container

Shao, Liu, and Liu, CAS, 2012

Fluent (up) vs SPH （bottom） Water level at an observation point

cos(2 / )S A t T

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3.7 Liquid sloshing – in a rotating rectangular container

Shao, Liu, and Liu, CAS, 2012 Shao, Liu, and Liu, CAS, 2012 Yang, Peng and Liu, IJCM 2011

1.0 rad s

8.2 rad s 4.1rad s

2.0 rad s 1.0 rad s

4.1rad s

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3.7 Liquid sloshing – Ballast water

Shao, Liu, and Liu, CAS, 2012 Shao, Liu, and Liu, CAS, 2012 Yang, Peng and Liu, IJCM 2011 Yang, Peng and Liu, IJCM 2011

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3.7 Liquid sloshing – in other shapes of containers

Shao, Liu, and Liu, CAS, 2012 Shao, Liu, and Liu, CAS, 2012 Yang, Peng and Liu, IJCM 2011 Yang, Peng and Liu, IJCM 2011

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Shao, Liu et al., EC, 2015.

Vertical baffle

Horizontal … Porous …

Multiple compartments

M>T>I>-

3.7 Liquid sloshing – sloshing mitigation

3. SPH for hydrodynamics – FSI problems 41/68

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3.8 Boom and oil spill — Rigid boom

•Free surfaces

•Multiphase

•Fluid-solid interaction

•Wave-current

Yang and Liu, SCPMA 2012

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Evolution of flow pattern

Frontal area and two ends

Drag force

Flow pattern

Criterion for stability

0.41

( ) arctan( )

x

x

L

L

Lu C u

L

2 VD U Urigid：V = 0

flexible：V = -2/3

3.8 Boom and oil spill — Flexible boom (SPH+EBG)

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Yang & Liu, PRE, 2015; JHD, 2016.


3.9 Hydro-elasticity – dam collapse with elastic plate

Displacement of plate free end

Water level

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Shao & Liu, JHD, 2013.

4. SPH for environmental flows 4.2 Landslide

• Fast landslide – flow like

• Fluid model – non-Newtonian

• Surface topography – GIS data

Tangjiashan Landslide: Pre- and post-earthquake topographies.

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Hu, Liu et al., Environmental Earth Sciences, 2015.

4. SPH for environmental flows 4.2 Landslide

3D profile SPH model of Tangjiashan landslide

Pre- and post-earthquake topographies

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Hu, Liu et al., Environmental Earth Sciences, 2015.

4. SPH for environmental flows 4.4 Subsurface flows – porous media

SPH simulation Comparison: SPH (top) and VOF (bottom)

Multiphase flow in a fractured porous media

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Liu et al., Water Resources Research, 2007.

4. SPH for environmental flows 4.4 Subsurface flows – fracture network

Multiphase flow in a fracture network

DPD模拟 VS VOF模拟

SPH VS VOF、Experiment

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49

5. SPH for explosion and impact 5.1 1D TNT slab detonation

Liu et al., Shock Waves, 2003

TNT 0.1 m

Ignition point

Solid boundary

Detonation direction

TNT slab detonation

x(m)

P(G

Pa)

0 0.02 0.04 0.06 0.08 0.1

5

10

15

20

25 Von Neumann Spike

C-J State Pressure

Ideal explosive

Non-ideal explosive


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5. SPH for explosion and impact 5.2 2D confined UNDEX

Liu et al., C&F, 2003

Pressure field Bubble evolution

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5. SPH for explosion and impact 5.3 Water mitigation (WM)


Water held in plastic bags as a bomb shelter to mitigate blast effects

0 0.25 0.5 0.75 1 1.25 1.5 1.75 20.4

0.5

0.6

0.7

0.8

0.9

1

Normalized water shield thickness

Nor

mal

ized

pea

k sh

ock

pres

sure

Point 4Point 3Point 2Point 1

Peak shock pressure

0.5

0.0

25

HE

Water

Air

P1 P2 P3

P4

Contact WM

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5. SPH for explosion and impact 5.4 Middle & high velocity impact


2D Taylor bar impact with adaptive SPH

3D Taylor bar impact with SPH

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5. SPH for explosion and impact 5.5 Penetration


Aluminum

6180 m/s

10 c

m

0.4 cm

D=1 cm

Al disk impacting/penetrating al plate at 6180 m/s

Other examples

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5. SPH for explosion and impact 5.6 Contact explosion

Feng & Liu, Shock Waves, 2013

钢板

TNT炸药

D1 D2

The shape of the crate is closely related to type, size and shape of the explosive charge

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5. SPH for explosion and impact 5.7 Shape charge with jet formation

Feng & Liu, C&F, 2013

高能炸药引信

外壳

药型罩装药直径

装药头长空腔长度

装药长度

外壳厚度

锥角

Metal jets

Simulation

Experiment

Metal jets without & with metal case

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5. SPH for explosion and impact 5.7 Shape charge with jet formation & penetration

T (s)

Ene

rgy

(MJ)

0.0E+00 5.0E-05 1.0E-04 1.5E-04

Kinetic EnergyInternal EnergyTotal Energy

10

15

20

25

30

5

Feng & Liu, C&F, 2013

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5. SPH for explosion and impact 5.8 Explosive-driven welding

v

Welding from direct impact Deribas (1967), Hydrodynamic model

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5. SPH for explosion and impact 5.8 Explosive-driven welding

Explosive-driven welding

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6. Prospects and future directions

Better theories Relationship between particle-particle interactions,

Theoretical foundation for multi-scale modeling,

Fluid-solid interaction model.

Applications:

Protective technology,

Coastal engineering and ocean hydrodynamics,

Civil and environmental engineering,

Bio/nano engineering,

Movie and animation making…

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60


Target：3D SPH code for FSI with wave and currents

1 Features • 2 and 3D • Lagrangian, particle method • Nonlinear • Explicit algorithm • Multi-materials, Multi-scales,

Multi-physics

2 Typical applications • Free surface flows（breaking waves、

dam collapse, flood…）

• FSI（slamming、sloshing、water-on-deck、 high speed water entry/exit）

• Extreme load（explosion, impact, penetreation）

2 Advantages • Meshfree: easy in treating large

deformation • Lagrangian particle: easy in

treating free surfaces and moving interfaces.

• FSI: simutaneously coupling

Code • Released the first SPH open source code； • Developing a 3D SPH code for hydrodynamics and

environmental flows

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Coupling approaches: 1. Coupling SPH/DEM for problems with solid particles (landslide, e.g.),

landslide mud flow

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Coupling approaches: 2. Coupling particle methods with FEM/FDM for boundary enhancement

and fluid-solid interaction,

SPH+FEM modeling 911

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Coupling approaches: 3. Coupling MD/DPD/SPH for multi-scale simulation,

Multi-scale modeling：from nano to micro and to macro scale

DPD particles

MD atoms SPH particles

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Coupling approaches: 4. Coupling multiple physics (viscous, elastic, heat, chemical,

electronic…).

Electrochemical Phenomena: Induced Polarization

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Collaborators

G. R. Liu, Univ. Cincinnati

W. K. Liu, NWU

Paul Meakin, H. Huang, INL

S. K. Tan, NTU

Z. Shang, Daresbury Lab, UK

Team members

X. Wen, Z. L. Zhang, P. Y. Yang, PKU

J. R. Shao, X. F. Yang, …,Imech

Z. Chen, G. X. Zhu, DLUT

L. Cheng, SCU

J. Z. Chang, H. T. Liu, …, NUC

Chinese Academy of Sciences

NSFC, China

LMFS，LNM, LHMRE

Funding organizations

National University of Singapore (NUS)

A-Star, Singapore

DSTA, Singapore

Idaho National Laboratory (INL)

DoE, US

Lee Kuan Yew (LKY) Foundation

Acknowledgement 65/68

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Documents

Smoothed Particle Hydrodynamics - Methodology and … · 2019-11-06 · M. B. Liu (刘谋斌) [email protected] . November 30, 2016 @NTU. Recent Progress on meshless methods for Flow