Adaptive Tetrahedral Remeshingfor Multiphase Flow Simulations in

OpenFOAM

Sandeep Menon and David P. Schmidt

Multiphase Flow Simulation LaboratoryUniversity of Massachusetts Amherst

June 3, 2009

Off-center Droplet Collision

M. Dai and D. P. Schmidt,

“Numerical Simulation of Head-On Droplet Collision: Effect of Viscosity on Maximum Deformation”,

Phys. Fluids, 17(4), 2005.

Motivation

Pros and Cons:Accurate interface representation.Direct application of interface boundaryconditions.Conserves mass very well.Complicated mesh manipulation withlocalized remeshing and interpolation.

Lagrangian interface tracking:Interface points move with the interfacenormal velocityThe interior mesh automatically adjusts tomaintain mesh qualityWe only use simplical meshes

Prior Work

Since last year:Two-dimensional version in OF completedDemonstrated for ink jetsPublished in ILASS 2008, ICLASS 2009

Interface tracking capabilities in OpenFOAM:interTrackFoam - Prior work on interfacetracking by Zeljko Tukovic and Hrvoje Jasak.Uses the freeSurface library, also developedby Tukovic and Jasak.Used mesh-motion only - limited deformationcapability.tetDecomposition mesh motion solver.

Three Major Code Components

Incompressible PISO solverMesh motionMesh reconnections

Tetrahedral Mesh Motion

Current state of techniques:Laplacian smoothing - fast,simple, but createsdegenerate cells.Need to associate meshmotion with mesh quality.Alternative:optimization-basedsmoothing.Optimize algebraic meshquality metrics.More expensive thanLaplacian smoothing, butvery effective.

Tetrahedral Mesh Motion

Mesquite Optimization Library:Developed by Sandia NationalLabs.OpenFOAM wrapper class -mesquiteSmoother.Run-time selection of:É Optimization algorithms: CG,

Steepest Descent, FeasibleNewton, Quasi Newton, etc.

É Quality metrics: ConditionNumber, Inverse Mean Ratio,Aspect Ratio, etc.

É Termination Criteria: RelativeQuality Improvement, L2 norm,iterations, CPU Time, etc

Mean Ratio =12(3V2)1/3∑6

iL2e

Atomic Topology Operations

Arbitrary number of tetrahedra sharing an edge.Dynamic Programming algorithm to define swap configuration.

3D Edge Flip2D Edge Flip

Combination of Swap Operations

3-2 swapEquitorial Polygon2-3 swap4 cells sharing an edge

Possible Configurations

7 sides, 42 ways

6 sides, 14 ways5 sides, 5 ways

Tetrahedral Bisection and Collapse

Test Case: Rotating & Translating Sphere

Test Case: Rotating & Translating Sphere

Test Case: Rotating & Translating Sphere

Ink Jet Simulation

Conclusion

Future work...Automated interface topology modifications for dropletbreak-up and coalesence.Effective divergence-free local interpolation.Hybrid parallelization efforts: MPI and pthreads.

Work In Progress...Non-Newtonian effects.Temperature-dependent viscosity and surface-tension effects.