Fully Implicit TwoWay Coupling of Fluids and Solids

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Fully Implicit Two-Way Coupling of Fluids and
Solids

• Avi Robinson-Mosher

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Collaborators

• Tamar Shinar
• Jon Grétarsson
• Jonathan Su
• Ron Fedkiw

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Our Method

• Eulerian fluids
• Multiphase, incompressible flow
• Lagrangian solids
• Rigid and deformable
• Volumes and shells
• Lumping fluid onto solid

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Fluid Simulation

• Incompressible flow

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Fluid Simulation

• Projection method

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Simple Example

• Two materials in a single cell
• Enforce contact condition and take implicit
  approach to impulse transfer between materials

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Simple Example
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Momentum conservationin a single cell
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Momentum conservationin a single cell
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Mapping Nonaligned Grids

• WT performs a conservative mapping from dual
  cells to solid surface nodes
• W interpolates from solid surface nodes to dual
  cells

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Solid Simulation

• Solid momentum equation

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Lumped Momentum Equation
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Lumped Momentum Equation
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Alternative Formulation

• Enforce fluid momentum equation simultaneously

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Three Types of Dual Cells

• Full fluid dual cells
• Standard projection method
• Full solid dual cells
• No fluid
• Mixed dual cells
• Fluid mass lumped onto solid nodes

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Linear System

• Manipulations necessary for symmetry
• Scale fluid rows by V
• Negate solid rows

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Properties of Linear System

• Strongly indefinite
• (1,1) block is positive definite
• (2,2) block is negative definite

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Solving Linear System

• Symmetry allows solution with fast solvers
  (MINRES, Paige and Saunders)
• Indefiniteness forbids use of Conjugate Gradients

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Preconditioning Linear System

• MINRES requires symmetric positive definite
  preconditioner
• We use block diagonal preconditioner
• Standard IC(0) preconditioner for (1,1) block
• Diagonal preconditioner for (2,2) block

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Similarity to Stokes Flow

• Galerkin matrix

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Symmetric QMR

• Recently tried using symmetric QMR (Freund and
  Nachtigal)
• Allows use of indefinite preconditioner
• Superior convergence

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Time Integration

• F1
• Time n1/2 fluid velocities
• S1 Coupled solve
• Time n1/2 solid velocities
• Time n1 solid positions
• F2
• Find leak-proof time n fluid velocity
• F3
• u fluid velocity

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Time Integration

• S2 Coupled solve
• Solid velocities to time n1
• Fluid pressures
• F4
• Divergence free time n1 fluid velocity

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Parallelization

• Lower-dimensional boundary
• One processor for solid
• Fluid broken into blocks

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Future Work

• Non-aligning meshes
• Slip boundary conditions
• Asynchronous or fully implicit solids
• Time step limitations

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Examples

• Some examples produced with our method,
  illustrating what it can do

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Buoyancy
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Rigid Solids and Shells
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Many rigid bodies
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Many rigid bodies
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Deformable Bodies
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Cloth
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Cloth Bag
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Smoke Balloon
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Articulated Solids
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Thank you
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Motivation

• Application areas
• Discussion of previous methods

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Previous Methods

• Computer Graphics
• Guendelman
• Bridson
• Klingner
• Chentanez

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Previous Methods

• Computational Physics
• Immersed boundary
• Immersed interface
• What else?