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Immersed Boundary Surface Method infoam-extend
Hrvoje Jasak
Wikki and University of Zagreb
OpenFOAM in Hydraulic Engineering Conference
BAW Karlsruhe, 21-22/Nov/2018
Immersed Boundary Surface Method in foam-extend – p. 1
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Outline
Objective
• Present the new (stabilised) formulation of the Immersed Boundary Method in
foam-extend: Immersed Boundary Surface (IBS)
• Provide examples from hydraulic engineering
Topics
• Background: Immersed Boundary Method in foam-extend
• New algorithm: Immersed Boundary Surface (IBS) Method
• Imposition of boundary conditions
• Validation: Simple static mesh cases
• Handling IBS motion: Dynamic IBS
• Validation: Dynamic mesh cases
• Hydraulic engineering example: ONR Tumblehome
• Summary
Immersed Boundary Surface Method in foam-extend – p. 2
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Background
Immersed Boundary Method in foam-extend
• Implementation of the Immersed Boundary Method (IBM) is based on polynomial
fitting of the solution with respect to the boundary condition
φP = φib + C0(xP − xib) + C1(yP − yib)
+ C2(xP − xib)(yP − yib) + C3(xP − xib)2 + C4(yP − yib)
2
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Fluid cells
Solid cells
IB cells
IB points
Extended stencilP
ib
• The IBM performs satisfactorily in single-phase flows, but carries some drawbacks:
handling of Neumann boundary conditions, wall function implementation
• In free surface flows, the solver shows strong instability due to matching of
gradients next to the IB surface
Immersed Boundary Surface Method in foam-extend – p. 3
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Background
Project Objective
• Objective: provide a robust and efficient Immersed Boundary capability for naval
hydrodynamics simulations, specifically for motion of floating objects in confinedspaces
Functional Analysis
• While functionally correct, the idea of polynomial fitting is adequate for smoothly
varying solution variables in single-phase flows
• Handling of Neumann boundary conditions at the IB was unsatisfactory: fitting
condition cannot be fully implicit, yielding instability
• Wall function implementation carries some uncertainty due to log-law fitting
• A free surface indicator such as Volume-of-Fluid cannot be adequately fitted and
leads to instability
• Attempts to use the Level Set free surface capturing and the Ghost Fluid Method
for interface handling proved superior over the original method, but was not
completely satisfactory: alternative solution is sought
• Immersed surface data is evaluated on the STL: resolution-dependent
Conclusion: further improvement in robustness and accuracy is sought regarding
the precision and stability of discretisation at the IB surface
Immersed Boundary Surface Method in foam-extend – p. 4
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Immersed Boundary Surface
Immersed Boundary Surface
• IB implementation relies on the imposition of the boundary condition in the bulk of
the mesh: this is built into the discretisation matrix
• Old implementation loses information in the cut cell: reduction in volume; loss of
precision at the intersection
• Objective: implement the influence of the presence of a boundary within the mesh
as if the mesh is body-fitted:
◦ Introduce the “new” IB face in the cut cell
◦ Account for the partial cell volume without loss of accuracy
◦ Account for partial face areas without loss of accuracy
◦ Calculate face and cell centre consistent with cell cut
• . . . without changing the geometric mesh at all!
Immersed Boundary Surface Method in foam-extend – p. 5
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Immersed Boundary Surface
Immersed Boundary Surface: Finite Volume Support
• The FVM method operates on the following geometrical data
1. Cell-to-face connectivity: owner/neighbour addressing
2. Cell volumes and face area vectors
3. Interpolation factors and delta-coefficients (1/distance)
• . . . and nothing else!!! All data contained in fvMesh class
Implementation Rationale
• Introduce new IBS faces: intersected cells via distance functions
• Cell-to-face addressing, face area and face centre calculated from intersection
• For affected cells, FV data (above) is adjusted
Notes
• Underlying mesh connectivity remains the same after cutting
• Cut cell re-uses discretisation matrix slot of the original cell
• New faces created as 1-per-cut-cell and contained in the immersed patch:
face-cell addressing identifies cut cells
Immersed Boundary Surface Method in foam-extend – p. 6
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Immersed Boundary Surface
Immersed Boundary Surface: Old and New Methodology
Fluid cells
Solid cells
IB cells
IB points$\n$
Fluid cells: untouched
Solid cells: deactivated
IBS: intersected cells
Adjusted IBS centres
Characteristics of IBS Implementation
• Immersed boundary patch is included into the mesh via the distance function: all
cells that straddle the immersed boundary remain active
• STL resolution or quality is not important: only using nearest distance
• As the immersed boundary sweeps the cell, the “live” part of the cell remains well
defined: positive face-to-cell distance
• Convex cell cut by a zero-distance plane remains convex: no discretisation issues
Immersed Boundary Surface Method in foam-extend – p. 7
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Immersed Boundary Surface
Immersed Boundary Surface: Modified Immersed Boundary Cells
Background cell Background cell
Corrected face centre
Corrected cell centre
Immersed face centre
• Nearest distance calculated for vertices of all affected cells
• Intersection is calculated for all faces and cells: replace original data with
centres/areas/volumes of the “live part”
• Immersed intersection calculated based on point distance
◦ All faces and cells are cut by a distance plane
◦ Simple planar cutting provides robustness: no feature edges
• Near-wall distance calculated from live cell centre to immersed face
• Delta coefficients and interpolation factors corrected for centre position
Immersed Boundary Surface Method in foam-extend – p. 8
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Immersed Boundary Surface
Immersed Boundary Surface: Imposition of Boundary Conditions
• Immersed boundary is represented in the mesh by STL intersection with cells
• Therefore, conventional boundary condition implementation suffice on the
immersed patch for a static mesh and IB surface
• Immersed boundary motion involves change in intersection: number of IB faces
changes!
• Evaluation of immersed properties is performed without interpolation or
simplification
• STL surface is automatically refined/coarsened to comply with the background
mesh: automatic coarsening and refinement
Immersed Boundary Surface Method in foam-extend – p. 9
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Immersed Boundary Surface
Calculation of IB Intersection: Degenerate Surface Cutting Cases
• “Regular intersection” occurs between a cell and STL surface
• Due to finite accuracy, STL regularly coincides with faces or does not provide
accurate intersection
◦ Direct face intersection between Dry and Wet cell: face becomes IB face
◦ Inaccurate intersection of STL feature edges/points may yield a geometrically
open cell, with possible robustness issues
◦ Using the Marooney Maneouvre to guarantee a closed cell after cutting
∑C
sf = 0 for a regular cell
∑C
γf sf + sf IB = 0 for an intersected cell
where γf is the area correction, obtained by cutting
◦ Corrected IB face area sf IB is:
sf IB = −
∑C
γf sf
Immersed Boundary Surface Method in foam-extend – p. 10
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Static Mesh Validation
Static Mesh Immersed Boundary: Laplace Equation, Potential Flow
Immersed Boundary Surface Method in foam-extend – p. 11
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Static Mesh Validation
Static Mesh Immersed Boundary Cases: Laminar and Turbulent Flow
Immersed Boundary Surface Method in foam-extend – p. 12
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Static Mesh Validation
Static Mesh Immersed Boundary Cases: Free Surface Flow
• Free surface flow with the Ghost Fluid Method
• Cylindrical Immersed Boundary obstacle at the bottom, intersecting with boundary
Immersed Boundary Surface Method in foam-extend – p. 13
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Moving Immersed Boundary
Moving Immersed Boundary Surface Support
• Moving mesh Finite Volume Method uses a compensated form of the transport
equation
∫V
∂φ
∂tdV +
∮S
φ [n•(u− ub)] dS −
∮S
γ(n•∇φ) dS =
∫V
qv dV
where ub is the boundary velocity
• Motion consistency requires auxiliary “Conservation of Space” condition
∫V
∂V
∂t−
∮S
(n•ub) dS = 0
• Discretised space conservation law yields
V n − V o
∆t−
∑f
Fb = 0
Immersed Boundary Surface Method in foam-extend – p. 14
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Moving Immersed Boundary
Calculation of Cell Volumes and Motion Fluxes For Immersed Cells
• Volume swept by immersed face is calculated from new IB face and motion
distance.
Vb = xb•sfn volume swept in red
where xb is geometrical motion distance from old to new STL
• As the intersected area changes, swept volume must be distributed:
◦ Cell A: expand from cut volume to full volume: no IB face in new configuration
◦ Cell B: cut both at new and old configuration: IB face present
◦ Cell C: expand from zero volume to partial volume: IB face present
◦ (Cell D): expand from zero to full volume (cell fully swept by IB): no IB face
Volold
Volnew
volume swept byimmersed face
CELL B
New Position
Old Position
CELL C
CELL ACELL C
Immersed Boundary Surface Method in foam-extend – p. 15
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Dynamic Mesh Validation
Dynamic Mesh Validation: Single-Phase Flow
• Moving immersed boundary within a static mesh
• Laminar Flow, Re = 50
• Some noise in viscous force signal in small cut volumes
Immersed Boundary Surface Method in foam-extend – p. 16
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Dynamic Mesh Validation
Dynamic Mesh Validation: Moving Mesh Free Surface Flow
• Free surface capturing, VOF equation, Ghost Fluid Method
• Floating body described by Immersed Boundary Surface
• Prescribed motion: heave and sway motion
• Small oscillation in force related to viscous terms. This can be adjusted with mesh
refinement
Immersed Boundary Surface Method in foam-extend – p. 17
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Adaptive Refinement, Load Balance
Example: 6-DOF Free Floating with Adaptive Refinement and Load Balancing
• Force spikes caused by sharp corners on STL geometry: not a good idea
Immersed Boundary Surface Method in foam-extend – p. 18
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Verification: Resistance Forces
ONR Tumblehome Ship Hull: Body-Fitted vs Immersed Boundary
• ONR Tumblehome Ship from the Tokyo 2015 Workshop on Naval Hydrodynamics
• Bare hull in full scale at Fr = 0.2
• Comparison of a body fitted mesh simulation and immersed boundary
• No dynamic sinkage and trim, and no turbulence modelling (still working on that)
• Result: Resistance comparison
Mesh structure Resistance [kN]
Body Fitted Mesh 98.0 kN
Immersed Boundary 92.0 kN
• Notes
◦ The complete hull is modelled as Immersed Boundary
◦ No near-wall prismatic layers: wall functions see fluctuating y+
◦ Immersed boundary solver significantly faster: no small cells for CFL limit
◦ Intended use for IB patches are appendage geometries, not the complete hull
Immersed Boundary Surface Method in foam-extend – p. 19
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Verification: Resistance Forces
ONR Tumblehome Ship Hull: Body-Fitted vs Immersed Boundary
Immersed Boundary Surface Method in foam-extend – p. 20
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Verification: Resistance Forces
ONR Tumblehome Ship Hull: Body-Fitted vs Immersed Boundary
Immersed Boundary Surface Method in foam-extend – p. 21
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Verification: Resistance Forces
ONR Tumblehome Ship Hull: Body-Fitted vs Immersed Boundary
Immersed Boundary Surface Method in foam-extend – p. 22
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Summary
Summary: Immersed Boundary Surface
• New implementation of Immersed Boundary Surface performed within the project
• Immersed Boundary created as a set of cell-to-STL intersection faces, capturing
all effects of the STL on underlying mesh: no simplifications!
• Significant improvement in robustness, accuracy, boundedness of the solution and
stability of the code
• For static mesh cases, conventional boundary conditions can be used
• Automatic adaptation of the triangular mesh: conforming with background mesh
intersection
Summary: Validation and Verification
• Validation and verification on static mesh and moving immersed boundary
presented for single-phase and free surface flows
Summary: Adaptive Refinement and Dynamic Load Balancing
• Adaptive refinement uses a newly developed refinement class operating on
polyhedral cells
• Refinement criterion: distance from immersed boundary; limited to 2-3 levels
• Dynamic load balancing: improved efficiency on massively parallel cases
Immersed Boundary Surface Method in foam-extend – p. 23