SPH: Why and what for? - Centrale...

SPH: Why and what for?David Le Touzé, Fluid Mechanics Laboratory, Ecole Centrale de Nantes / CNRS

4th SPHERIC training day

SPH

What for and why?

How it works?

Why not for everything?

Duality of SPH


SPH

Smoothed Particle Hydrodynamics

Particle method Liquids in motionRegularizingfunction

A fluid dynamics problem seen as a system of masses (particles) using a regularizing function.

Mainly applied to simulations ofAstrophysical fluidsStructure


SPH

Smoothed Particle Hydrodynamics

Particle method Liquids in motionRegularizingfunction

A fluid dynamics problem seen as a system of masses (particles) using a regularizing function.

Mainly applied to simulations ofAstrophysical fluidsStructureFree-surface flows

What is common to theseapplications?


SPH

What for and why? Free surface flowsViolent Fluid-Structure InteractionsStructures and Astrophysics

How it works?


Duality of SPH



What for and why? Free surface flows

Lagrangian meshless method: flexibilityno need for handling / adapting a mesh (high human cost)no convective term modeling: adapted to fast dynamics flows (violent impacts, shocks, explosions…)

Fast dynamics!!!



Slamming impact

experiment in the ECN tank

force (bow impact case)

3 million particles

6m/s impact

250m long ship at real scale

SPH-flow simulation



Lagrangian meshless method: flexibilityno need for handling / adapting a meshno convective term modeling: adapted to fast dynamics flows (violent impacts, shocks, explosions…)naturally handles large deformations of the fluid domain:

large motion of (multi-)bodiescomplex free surface (multi-breaking…) accurately resolved by modeling water only

Fast dynamics!!!


What for and why? The example of free surface flows

collaboration with INSEAN

Benchmarks of 1st

SPHERIC Workshop, Rome, May 2006

SPH-flow(red)

vs.

experiment(black)

force

velocity

with 80,000 particles only

with 1 million particles =>

force

velocity


What for and why? Free surface flows… and FSI

Lagrangian meshless method: flexibilityno need for handling / adapting a meshno convective term modeling: adapted to fast dynamics flows (violent impacts, shocks, explosions…)naturally handles large deformations of the fluid domain:

large motion of (multi-)bodiescomplex free surface (multi-breaking…) accurately resolved by modeling water only

permits non-diffusive interface multi-fluid modeling

explicit resolutionrobustness‘easy’ parallelisation by domain decompositionCPU cost per time step is O(N)

a variety of constitutive laws can be used within the same SPH solver=> multi-physics (fluid-structure interaction in strong coupling, multi-phases…)

compressible formalism

Fast dynamics!!!


What for and why? Violent Fluid-Structure Interactions

SPH in the fluid (whatever the structure description)meshless: no mesh adaptation/remeshing neededexplicit: time steps already small with low CPU cost per time stepLagrangian: adapted to violent FSI

SPH/SPH model:monolithic approach not limited to simple situationsno interface handling procedure neededviolent FSI up to fracture can be modelled

=> strong coupling and easy implementation

SPH/FEM coupling:benefit from the large variety of existing FEM structure modelseasy interface handling (compared to FSI with mesh-based eulerian fluid method)faster resolution than SPH/SPH

=> a good compromise for « moderately violent » FSI

Fast dynamics!!!


What for and why? Structures and Astrophysics

Structuresmeshless: no mesh adaptation/remeshing neededexplicit: time steps already small with low CPU cost per time stepLagrangian: adapted to violent deformations up to fracture

=> rigid body/body impacts, multi-material simulations, explosions…

AstrophysicsLagrangian: able to follow complex formationsEasiness of having many orders of magnitude

Fast dynamics!!!


What for and why?

1977 : Gingold & Monaghan / Lucy: SPHapplication field: astrophysicsmethodological background: statistics

80’s : mainly applied in astrophysicsstar and moon 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, molecular dynamics (polymers), biology (blood flows), metallurgy, aerodynamics (supersonic andhypersonic flows)…

SPH in free surface hydrodynamicsfast development:

SPHERIC ERCOFTAC Special Interest Group: created in 2005, counting 65 international member entities (academias + industrials)

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


SPH

What for and why?

How it works?


Duality of SPH



How it works?

Euler equations in Lagrangian formalism

Stress tensor form

Equation of state (Tait’s)

In the fluid


How it works?

Stress tensor form

Equation of state (Tait’s)

In the structure

( )20 0P c ρ ρ= −

PI Sσ = − +

20

0

Ecρ

=

12 ( )3

. .dS tr S Sdt

μ ε ε⎛ ⎞= − +Ω − Ω⎜ ⎟

⎝ ⎠


How it works?

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

Vii j


How it works?

interpolationconvolution using a kernel W (~test fonction)

interestestimation of the gradient from the values of the considered quantity

analytical


How it works?

explicit

C

‘‘particles’’fluid domain is splitted into volume elementsof constant mass which are followed in theirLagrangian motion

quadrature

time advance

=> intrinsicColagrossi,

Antuono, Le Touzé,

Phys. Rev. E, 2009


fluidparticles

‘ghost’particles

How it works?

principlesolid BCs are imposed thanks to mirrored particles


SPH

What for and why?

How it works?


Duality of SPH




Accuracy test: wave propagation

Standard SPH



Advection MUST dominate to ensure accurateresults, otherwisethey are poorwith standard SPH


SPH

What for and why?

How it works?


Duality of SPH



Duality of SPH

explicit

C


quadrature

time advance

=> SPH in fluid dynamics = discretisation scheme of PDEs using no explicit mesh connectivity


Antuono, Le Touzé,

Phys. Rev. E, 2009


Duality of SPH

explicit

C


quadrature

time advance

=> SPH in fluid dynamics = system of constant masses with conservation properties


Antuono, Le Touzé,

Phys. Rev. E, 2009


Duality of SPH

Symmetric interactions ensure conservation properties(Hamiltonian system with no dissipation, first two moments conserved)

System of masses

Possibility to use Finite Volume tools(Riemann solvers, non constant masses of the particles, ALE,…)

Discretisation scheme of PDEs


Duality of SPH

1D Riemann solver applied to each interaction couple (i,j)

exact solver (Godunov)

MUSCL scheme: linear extrapolation at the middle of (i,j) to increase convergence

shock tube problem

Riemann solver

i

j

left state right state


Duality of SPH

Accuracy test: wave propagation

Standard SPH SPH-flow


Duality of SPH

System of masses

Both views must be considered to understand why SPH works andits very specific numerical behavior

(no theory exists for proving the observed convergence of standard SPH on practicalproblems!)

Discretisation scheme of PDEs


Duality of SPH

Thanks for your attention

SPH: Why and what for? - Centrale...

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