Overview and Recent Developments of Dynamic Mesh Capabilities · Overview and Recent Developments of Dynamic Mesh Capabilities Henrik Rusche and Hrvoje Jasak [email protected]

Overview and Recent Developments ofDynamic Mesh Capabilities

Henrik Rusche and Hrvoje Jasak

[email protected] and [email protected]

Wikki Gmbh, Germany

Wikki Ltd, United Kingdom

6th OpenFOAM Workshop, State College, USA, 13-16 June 2011

Overview and Recent Developments of Dynamic Mesh Capabilities – p. 1

Introduction

Objective

• Review existing dynamic mesh techniques and new developments as implementedin OpenFOAM

Topics

1. Dynamic Mesh Class & Topological Changes

2. Traditional Techniques: Automatic Mesh Motion and Topological Changes

3. Radial Basis Function in Mesh Motion and Morphing

4. Alternatives to Dynamic Mesh

5. Fluid-Structure Interaction Examples

6. Summary


Background: Dynamic Mesh Class

Dynamic Mesh Handling in OpenFOAM

• Dynamic mesh handling is well established in OpenFOAM: moving boundarieswith dynamic mesh deformation, 6-DOF solid body motion, cell layering andsliding, adaptive mesh refinement

• Techniques are powerful, validated and well established

◦ In-cylinder flows in internal combustion engines: moving piston and valves

◦ Turbomachinery simulations: rotor-stator interaction

◦ Naval hydrodynamics: floating bodies with 6-DOF solvers

◦ Fluid-structure interaction: deforming fluid mesh

Dynamic Mesh Class

• OpenFOAM is an excellent platform for complex physical modelling: dynamicmesh extends the scope to complex engineering geometries

• Common interface to all dynamically changing meshes

• In discretisation, all mesh changes reduce to point motion: cells and facesintroduced and removed at zero area/volume with no data mapping orconservation errors

• Concerns for the future: Extreme cases of domain deformatio n andease-of-use of topological mesh change engine and adaptivi ty


Traditional Techniques

Automatic Mesh Motion

• Motion will be obtained by solving a mesh motion equation , where prescribedboundary motion acts as a boundary condition

• Choices for a simplified mesh motion equation:

◦ Laplace equation with constant and variable diffusivity

∇•(k∇u) = 0

◦ Linear pseudo-solid equation for small deformations

∇•[µ(∇u+ (∇u)T ) + λI∇•u] = 0

• Works well, but fails in extreme rotation or deformation (eg. squish)


Traditional Techniques

Topological Mesh Changes

• Primitive mesh operations : add/modify/remove a point, a face or cell

• Topology modifier : package primitive operations under easy interfaces

◦ Attach-detach boundary

◦ Cell layer additional-removal interface

◦ Sliding interface

◦ Error-driven adaptive mesh refinement

• Dynamic mesh : combine topology modifiers and user-friendly mesh definition tocreate a dynamic mesh for a class of problems

• Examples: mixer mesh, 6-DOF motion, IC engine mesh (valves + piston),solution-dependent crack propagation in solid mechanics


Cross Flow Heat Exchanger

• Meshing each channel is not practical!

• Model as a three phase system with

◦ 2 sets Navier-Stokes equations with porous media terms◦ 2 turbulence models◦ 2 fluid enthalpy equations

◦ Solid heat conduction

• But where is the dynamic mesh?



• We utilise single domain approach to avoid mapping heat sources

• In this approach, the mesh goes through three states during segregated solution

1 2 3

fluid stream 1 solved fluid stream 2 solved solid solved

• Implementation uses Attach/Detach topological modifiers

• Single domain → block-solution of energy equations is an option






Radial Basis Function

Radial Basis Function Automatic Mesh Motion

• Mathematical tool which allows data interpolation from a small set of control pointsto space with smoothness criteria built into the derivation

• Used for mesh motion in cases of large deformation: no inverted faces or cells

• Control points chosen on a moving surface, with “extinguishing function” used tocontrol far-field mesh motion

• Implemented by Frank Bos, TU Delft and Dubravko Matijaševic, FSB Zagreb


Radial Basis Function

RBF Mesh Morphing

• RBF morphing object defines the parametrisation of geometry (space):

1. Control points in space, where the parametrised control motion is defined

2. Static points in space, whose motion is blocked

3. Range of motion at each control point: (d0,d1)

4. Set of scalar parameters δ for control points, defining current motion as

d(δ) = d0 + δ(d1 − d0), where 0 ≤ δ ≤ 1

• For each set of δ parameters, mesh deformation is achieved by interpolatingmotion of control points d over all vertices of the mesh: new deformed state of thegeometry

• Mesh in motion remains valid since RBF satisfies smoothness criteria

Using RBF in Optimisation

• Control points may be moved individually or share δ values: further reduction indimension of parametrisation of space

• Mesh morphing state is defined in terms of δ parameters: to be controlled by theoptimisation algorithm


Geometric Shape Optimisation

HVAC 90 deg Bend: Flow Uniformity at Outlet

• Flow solver: incompressible steady-turbulent flow, RANS k − ǫ model; coarsemesh: 40 000 cells; 87 evaluations of objective with CFD restart

• RBF morphing: 3 control points in motion, symmetry constraints; 34 in total

• Objective: flow uniformity at outlet plane

iter = 0 pos = (0.9 0.1 0.1) v = 22.914 size = 0.69282iter = 5 pos = (0.1 0.1 0.1) v = 23.0088 size = 0.584096iter = 61 pos = ((0.990164 0.992598 0.996147) v = 13.5433 size = 0.000957122


... even more alternatives

• Tetrahedral Edge Swapping (UMass Amherst)

◦ Tetrahedral cell quality examined while moving themesh: bad cells trigger local remeshing

◦ answers dynamicMesh interface

• Overset Grid (with Penn State)

◦ Multiple objects meshed body-fitted with overlap◦ Hole cutting algorithm to remove excess overlap

cells◦ Mesh-to-mesh interpolation with implicit updates

built into patch field updates and linear solverout-of-core operations

• Immersed Boundary Method (with U Zagreb and UCDublin)

◦ (Static) background mesh is intersected with thesurface representation of the objects

◦ Three cases are identified: fluid, solid andinterpolation cells

◦ Solid cells and interpolation cells require specialnumerical treatment


Fluid-Structure Interaction

Fluid-Structure Interaction Solver and Dynamic Meshes

• Current incarnation of the FSI solver is substantially more advanced from previousversions. Substantial new developments

◦ Large deformation formulation in absolute Lagrangian formulation

◦ Independent parallelisation in the fluid and solid domain

◦ Parallelised data transfer in FSI coupling

◦ Crack propagation with topological changes and self-contact

• New mesh motion and dynamic boundary handling techniques available

• Working on Immersed Boundary Method on both sides of FSI interface


Summary

Progress in Dynamic Mesh Handling in OpenFOAM

• There is no “one right way” to perform dynamic mesh simulatio ns inOpenFOAM : choose the best method for the problem

• Standard techniques are well established, robust and parallelised

• Continuing work on efficiency: motion equation technique is expensive!

• Community contributions expand the scope: new developers

New Techniques

• Radial Basis Function in mesh motion and mesh morphing

• Automatic re-meshing: tetrahedral edge swapping

• Overset grid technology

• Immersed boundary method


Documents

Overview and Recent Developments of Dynamic Mesh Capabilities · Overview and Recent Developments of Dynamic Mesh Capabilities Henrik Rusche and Hrvoje Jasak [email protected]