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SPH: Why and what for? 4 th SPHERIC training day David Le Touzé, Fluid Mechanics Laboratory, Ecole Centrale de Nantes / CNRS SPH What for and why? How it works? Why not for everything? Duality of SPH

SPH Smoothed Particle Hydrodynamics Regularizing function Particle method Liquids in motion A fluid dynamics problem seen as a system of masses (particles) using a regularizing function. Mainly applied to simulations of Astrophysical fluids Structure

SPH: Why and what for? 4 th SPHERIC training day David Le Touzé, Fluid Mechanics Laboratory, Ecole Centrale de Nantes / CNRS SPH What for and why? Free surface flows Violent Fluid-Structure Interactions Structures and Astrophysics How it works? Why not for everything? Duality of SPH

What for and why? Free surface flows 4 th SPHERIC training day Fast dynamics!!! Lagrangian meshless method: flexibility no need for handling / adapting a mesh (high human cost) no convective term modeling: adapted to fast dynamics flows (violent impacts, shocks, explosions )

What for and why? Free surface flows 4 th SPHERIC training day Slamming impact force (bow impact case) SPH-flow simulation experiment in the ECN tank 3 million particles 6m/s impact 250m long ship at real scale

What for and why? Free surface flows 4 th SPHERIC training day Fast dynamics!!! Lagrangian meshless method: flexibility no need for handling / adapting a mesh no convective term modeling: adapted to fast dynamics flows (violent impacts, shocks, explosions ) naturally handles large deformations of the fluid domain: large motion of (multi-)bodies complex free surface (multi-breaking ) accurately resolved by modeling water only

What for and why? The example of free surface flows Benchmarks of 1 st SPHERIC Workshop, Rome, May 2006 force force velocity SPH-flow (red) vs. experiment (black) velocity with 80,000 particles only with 1 million particles => collaboration with INSEAN

What for and why? Free surface flows and FSI Fast dynamics!!! Lagrangian meshless method: flexibility no need for handling / adapting a mesh no convective term modeling: adapted to fast dynamics flows (violent impacts, shocks, explosions ) naturally handles large deformations of the fluid domain: large motion of (multi-)bodies complex free surface (multi-breaking ) accurately resolved by modeling water only permits non-diffusive interface multi-fluid modeling explicit resolution robustness easy parallelisation by domain decomposition CPU 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

What for and why? Violent Fluid-Structure Interactions Fast dynamics!!! SPH in the fluid (whatever the structure description) meshless: no mesh adaptation/remeshing needed explicit: time steps already small with low CPU cost per time step Lagrangian: adapted to violent FSI SPH/SPH model: monolithic approach not limited to simple situations no interface handling procedure needed violent FSI up to fracture canbemodelled => strong coupling and easy implementation SPH/FEM coupling: benefit from the large variety of existing FEM structure models easy interface handling (compared to FSI with mesh-based eulerian fluid method) faster resolution than SPH/SPH => a good compromise for «moderately violent» FSI

What for and why? Structures and Astrophysics Fast dynamics!!! Structures meshless: no mesh adaptation/remeshing needed explicit: time steps already small with low CPU cost per time step Lagrangian: adapted to violent deformations up to fracture => rigid body/body impacts, multi-material simulations, explosions Astrophysics Lagrangian: able to follow complex formations Easiness of having many orders of magnitude

What for and why? 1977 : Gingold & Monaghan / Lucy: SPH application field: astrophysics methodological background: statistics 80 s : mainly applied in astrophysics star 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 and hypersonic flows) SPH in free surface hydrodynamics fast 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)

How it works? In the fluid Euler equations in Lagrangian formalism Stress tensor form Equation of state (Tait s)

How it works? In the structure Stress tensor form σ = PI + S ds dt.. 1 = 2 μ ε tr( ε) +ΩS SΩ 3 Equation of state (Tait s) ( ) 2 0 0 P= c ρ ρ c 2 0 = E ρ 0

How it works? V i i j 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

How it works? interpolation convolution using a kernel W (~test fonction) interest estimation of the gradient from the values of the considered quantity analytical

How it works? quadrature particles fluid domain is splitted into volume elements of constant mass which are followed in their Lagrangian motion time advance C => intrinsic Colagrossi, Antuono, Le Touzé, Phys. Rev. E, 2009 explicit

How it works? principle solid BCs are imposed thanks to mirrored particles ghost particles fluid particles

Why not for everything? Accuracy test: wave propagation Standard SPH

Why not for everything? Advection MUST dominate to ensure accurate results, otherwise they are poor with standard SPH

Duality of SPH quadrature particles fluid domain is splitted into volume elements of constant mass which are followed in their Lagrangian motion time advance C => intrinsic Colagrossi, Antuono, Le Touzé, Phys. Rev. E, 2009 explicit => SPH in fluid dynamics = discretisation scheme of PDEs using no explicit mesh connectivity

Duality of SPH quadrature particles fluid domain is splitted into volume elements of constant mass which are followed in their Lagrangian motion time advance C => intrinsic Colagrossi, Antuono, Le Touzé, Phys. Rev. E, 2009 explicit => SPH in fluid dynamics = system of constant masses with conservation properties

Duality of SPH System of masses Symmetric interactions ensure conservation properties (Hamiltonian system with no dissipation, first two moments conserved) Discretisation scheme of PDEs Possibility to use Finite Volume tools (Riemann solvers, non constant masses of the particles, ALE, )

Duality of SPH Riemann solver shock tube problem left state right state j i 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

Duality of SPH Accuracy test: wave propagation Standard SPH SPH-flow

Duality of SPH System of masses Discretisation scheme of PDEs Both views must be considered to understand why SPH works and its very specific numerical behavior (no theory exists for proving the observed convergence of standard SPH on practical problems!)

Duality of SPH Thanks for your attention