Overview and Recent Developments of Dynamic 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
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Overview and Recent Developments of Dynamic Mesh Capabilities · Overview and Recent Developments of Dynamic Mesh Capabilities Henrik Rusche and Hrvoje Jasak [email protected]
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Overview and Recent Developments ofDynamic Mesh Capabilities
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
Overview and Recent Developments of Dynamic Mesh Capabilities – p. 2
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
• 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
Overview and Recent Developments of Dynamic Mesh Capabilities – p. 3
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)
Overview and Recent Developments of Dynamic Mesh Capabilities – p. 4
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
Overview and Recent Developments of Dynamic Mesh Capabilities – p. 5
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?
Overview and Recent Developments of Dynamic Mesh Capabilities – p. 6
Cross Flow Heat Exchanger
• We utilise single domain approach to avoid mapping heat sources
• In this approach, the mesh goes through three states during segregated solution
• Single domain → block-solution of energy equations is an option
Overview and Recent Developments of Dynamic Mesh Capabilities – p. 7
Cross Flow Heat Exchanger
Overview and Recent Developments of Dynamic Mesh Capabilities – p. 8
Cross Flow Heat Exchanger
Overview and Recent Developments of Dynamic Mesh Capabilities – p. 9
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
Overview and Recent Developments of Dynamic Mesh Capabilities – p. 10
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
Overview and Recent Developments of Dynamic Mesh Capabilities – p. 11
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
Overview and Recent Developments of Dynamic Mesh Capabilities – p. 12
... 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
Overview and Recent Developments of Dynamic Mesh Capabilities – p. 13
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
Overview and Recent Developments of Dynamic Mesh Capabilities – p. 14
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
Overview and Recent Developments of Dynamic Mesh Capabilities – p. 15