1

Slideline modeling in the FLAG hydrocodeLA-UR 11-04993

MultiMat 2011, Arcachon, France

Mark “Mack” Kenamond*

Matthew “Matt” Bement*

*XCP-1, Computational Physics Division,Los Alamos National Laboratory, USA

2

LA-UR 11-04993

Outline

• FLAG overview

• Lagrange slide surfaces– Tangential (friction) forces– Normal (frictionless) forces

• Advanced slide surface features– Dynamic slide removal– Advective slip– Neumann ALE along slide surfaces

3

LA-UR 11-04993

FLAG Overview• Continuous development since 1996• 1D/2D/3D ALE code (Lagrange + remap)• Mesh:

– Arbitrary polyhedral unstructured meshes– Dendritic constraints– Parallel, domain-decomposed (OpenMPI)

• Hydro:– Burton compatible SGH– Prototype CCH scheme under

development (Burton)• Slide surfaces

– Parallel– Gap opening/closing– Friction

• Materials:– Void, gases, solids, plasmas, HE– Many EOS and features– Many strength models and features

• HE burn– Programmed and/or reactive burn– Separate reactant and product EsOS– Pseudo-reaction zone models– Reactant/product mixture models

• Mixture physics– Static and dynamic mix models– Ejecta capability

• Relaxers:– Numerous relaxer methods– Numerous relaxer controllers– Numerous relaxer BCs

• Remap:– 1st or 2nd order flux-based remap with FCT– Several numerical gradient operators– Several monotonicity treatments– Kinetic energy “fix-up”

• Multi-material closure models– “Null”, Tipton, SSD closure models

• Mesh reconnection– Free Lagrange SPLIT/UNSPLIT– Isotropic and anisotropic mesh refinement– Dynamic slide removal

• Output– GMV, Ensight visualization– VISAR and PDV probes– Numerous other diagnostic outputs

4

LA-UR 11-04993

What’s a slideline?• Also called “contact”• Enables a tangential velocity discontinuity between two bodies

– Contacting materials can slide against one another– Thin shear boundary layer can be approximated by a discontinuity

• Enables interaction of two disconnected meshes– Impacting solids: gaps close and open

• Friction and/or boundary layer viscosity can be modeled

Single slide surface

CuCe

LiF

Al

Epoxy

Fung

Flyer plate simulation in FLAG

5

LA-UR 11-04993

200.0m/s Cue Ball Velocity

6

LA-UR 11-04993

FLAG Slide Surfaces: Overview• Features:

– Fully unstructured meshes– Permits contact/sliding between two or more disconnected or self-contacting bodies– Gap closing and opening supported– Fully eliminates all predicted interpenetrations– Parallel– Two-body friction supported

• Operates on boundary vertex/facet data

• Search step– Predicts surface interpenetration/contact– What happens with no contact forces?– Identifies vertex/facet “contact pairs”

• Enforcement step– Tangential (friction) forces:

• Compute frictional forces based on user-specified model– Normal (frictionless) forces:

• Solves for corrective forces that will completely eliminate interpenetrations

• Neatly integrates with existing hydro– Only modification to hydro is additions to point forces– Coordinates and velocities are not directly modified

Vertex

Facet

Mesh

7

LA-UR 11-04993

Integration into FLAG hydro (SGH)

• Hydro solver computes nodal forces (momentum equation)

• Contact algorithm is called– Parallelism stuff– Search algorithm identifies all (facet,vertex)

contact pairs– Compute tangential (friction) forces– Compute normal (frictionless) forces– Contact forces added to hydro forces

• Hydro solver continues with modified forces

8

LA-UR 11-04993

Normal (frictionless) forces

• Purpose: Compute corrective normal contact forces for contact pairs and add to hydro point forces

• Uses iterative predictor-corrector, Lagrange-multiplier-based approach

– Lagrange-multipliers () are normal contact force magnitudes between [vertex,facet] pairs – these are the unknowns

– Facet normals are continuous along surface – Force directions are based on facet normal at

projected location of vertex• Solver begins with 1D solution for each pair,

then iterates:– Compute point action/reaction forces from

pair forces and add to hydro forces– Re-solve EOM to get new predictor geometry– Update contact pair penetration depths

(“gaps”) and force directions– Correct force magnitudes () based on

change in gap:

– Iterate N times (we use 3<N<6)

nfacetnvert ninterp

Predicted location

Projected location

npair = Pair force direction

gpair = “gap”

fpair = pair npair

),2min(,0max0

01

iii gg

g

9

LA-UR 11-04993

Normal force method extends to 3D

• Parallel: 4 processors (colors in left image)

• Explosively loaded plate with a gap

HE

PlateGap

Detonator

10

LA-UR 11-04993

Tangential (friction) forces• Purpose: Compute tangential forces based on

some friction model and add them to the hydro point forces

• All FLAG friction models use a 1D “helper” coordinate system

– Quantities from either side can be projected to the other side via this 1D system

– Areal mass, momentum, yield stress on surface B integrated over area of point on surface A and vice versa. Each slide surface point then knows the local state on both sides.

– Provides state for friction models (normal force, sticking force, sliding velocity, yield stresses, etc)

– 2D only– Not compatible with 3+ body contact

• Friction locally disabled when surfaces are “too far apart”

• Two friction models exist– Momentum coupling “friction” determines sticking

force and applies some fraction of this force. Single parameter model.

– “Standard” friction model includes dry friction (static and Coulomb friction with Stribeck effect) and a Couette-like viscous friction term

• Dry friction force limited by the yield stress of the weaker material

• Total friction force limited by sticking force

(x)

xB

A

t

umf

uuu

mu

mmm

lumpA

AstickA

AlumplumpA

lump

lumplump

BAlump

BAlump

,

,

,

*

*

B*

Sticking Force Example

LumpedMass

LumpedMomentum

LumpedVelocity

RelativeVelocity

StickingForce

11

LA-UR 11-04993

Advanced slide line features

• Combine ALE features with slide lines

• Add mesh reconnection

• Provides more advanced features– Dynamic slide removal– Advective slide surfaces and slide removal– Neumann BC along slide surfaces and slide

removal

• Effective when surface meshes tangle

12

LA-UR 11-04993

Dynamic slide line removal

• Can dynamically “stitch” two surfaces together• “Slave” surface points projected to “master”

surface• “Close” points are merged• Mesh connectivity is modified to connect the

surfaces using remaining points• Can result in “interesting” polygonal meshes• ALE is usually activated across the slide surfaces

after removal• 1D and 2D only, 2-body contact only

13

LA-UR 11-04993

Example: Dynamic slide removal

LagrangeSlideline

IdealGas=1

IdealGas=1

IdealGas=10

HighExplosive

– Lagrange slideline– Slideline removed half way through simulation– ALE activates after slide removal

14

LA-UR 11-04993

Movie

• Add movie

15

LA-UR 11-04993

Advective Slide Surfaces

• Slideline defined along two surfaces with identical, aligned discretizations

• Complete Lagrange step with slidelines• Relax points on one surface back to points

on other surface using ALE• Can alternate which surface is relaxed so

that both surfaces can be improved• Aligned surfaces can be removed without

introducing “interesting” polygonal meshes

16

LA-UR 11-04993

Example: Advective slides and slide removal

AdvectiveSlideline

IdealGas=1

IdealGas=1

IdealGas=10

HighExplosive

– Advective slideline– Slideline removed half way through simulation– ALE active always

17

LA-UR 11-04993

Movie

• Add movie

18

LA-UR 11-04993

Neumann ALE along slide surfaces

• Can relax points along a surface– A special relaxer BC exists: “Neumann”– It relaxes points along a surface defined by either a linear or cubic

B-spline fit to the surface points

• But flux-based remap has limits on relaxation displacements

• FLAG can subcycle remap multiple times per hydro cycle• Neumann BC and subcycling applied to move points large

distances along the surface in one hydro cycle– Surface representation at start of subcycling re-used– One surface can be moved so that its points align with points on

the other surface– Can then remove the slideline without producing “interesting”

polygonal meshes

19

LA-UR 11-04993

Example: Lagrange slides, Neumann BC and slide removal

LagrangeSlideline

IdealGas=1

IdealGas=1

IdealGas=10

HighExplosive

– Lagrange slideline

– Neumann BC re-aligns lower points to upper points

– Then remove slideline

– ALE activated during Neumann relaxation

20

LA-UR 11-04993

Movie

• Add movie

21

LA-UR 11-04993

Summary

• FLAG has a mature, flexible slideline capability• FLAG has many other capabilities• Combination of capabilities produces more advanced

slideline capabilities• Regularly applied to complex solid mechanics simulations• Sometimes applied by curious code developers to

pointless – but cool – simulations, such as . . .

22

LA-UR 11-04993 4.0km/s Cue Ball Velocity

23

LA-UR 11-04993 4.0km/s Cue Ball Velocity

24

LA-UR 11-04993

Backup slides

25

LA-UR 11-04993

Search• Purpose: Identify [vertex,facet] pairs that

will be or are in contact this cycle– Results are used by the enforcement

algorithm to compute corrective contact forces

• Uses Parallel-Pronto3D-like predictor-based search algorithm

• Predictor configuration based on surface deformations without contact forces

– Surface geometry at n and predictor geometry at n+1 used to identify contact

• Inexpensive neighborhood search identifies candidate pairs that likely contact

– Screens majority of non-contacting pairs from more expensive detailed search

• Detailed search identifies pairs that actually contact

– Most challenging component of the entire slide surface algorithm

Geom @ n Predicted geom @ n+1

@ n+1

@ n

Facet boxes bound n and n+1

Four pairs

Geometry at n and n+1

Detailed inspection Two pairs

Not easy!

26

LA-UR 11-04993

FLAG Slide Surfaces: Parallelism

• Purpose: Provide each processor with necessary set of facets and vertices to correctly solve for contact forces

• Meshes are domain decomposed– Each processor only owns a portion of the global mesh– Therefore, it only owns a portion of a slide surface

• Slide surface algorithm needs “ghost” copies of off-processor vertices and facets– If a local (on-processor) vertex might contact a non-local (off-

processor) facet, a ghost copy of the facet must be generated, locally

– If a ghost copy of a facet is required, so are its connected vertices

• General Process:– Each cycle, check if processors have the ghost copies they need– If any processor lacks a needed ghost facet, all processors will

compute and communicate new sets of ghost copies – I call this “reghosting”

27

LA-UR 11-04993

Ghost check

• Determines if “reghosting” is necessary• Check made every cycle before search• Compute facet bound boxes for all

local (non-ghost) facets– Same bound boxes as neighborhood

search

• Construct processor bound box containing all local facet bound boxes

• Communicate processor bound boxes to all processors

• If a local facet bound box overlaps some other processor’s bound box, and that other processor lacks a ghost copy of this facet, all processors will re-compute ghosts

• Result is “Yes, reghost” or “No, ghost data are okay”

Initial (@ n)

Predicted (@ n+1)

Local facet bound box

Processor bound box

Local facet

Initial local surface(@ n)

Predicted local surface(@ n+1)

28

LA-UR 11-04993

“Reghosting”• Compute “augmented” facet bound boxes

– Project vertices N cycles into future: xn+N ~ xn+N vntn

– User chooses N (default is N=50)

– Calculate facet boxes that bound facet in initial and projected states

• Compute “augmented” processor bound boxes

– Box bounds all local augmented facet bound boxes

• Communicate augmented processor boxes to all processors

• If a local, augmented facet box overlaps with some other processor’s bound box, that other processor requires a ghost copy of this facet

• If another processor requires a copy of a local facet, it must also have copies of the vertices defining that facet

• Projecting N cycles decreases reghosting frequency, but increases number of ghosts

Initial (@ n)

Projected (@ n+N)

Augmented local facet bound box

Augmented processor bound box

Local facet

Initial local surface(@ n)

Projected local surface(@ n+N)