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Smoothed Particle Hydrodynamics For Deformable Vessel Dynamics

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Smoothed Particle Hydrodynamics For Deformable Vessel Dynamics Progress Report Van Jones 2008/01/30 Research Goals Near Term: Rigid-Body Dynamics with 3 Degrees of ... – PowerPoint PPT presentation

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Title: Smoothed Particle Hydrodynamics For Deformable Vessel Dynamics


1
Smoothed Particle Hydrodynamics For Deformable
Vessel Dynamics
  • Progress Report
  • Van Jones
  • 2008/01/30

2
Research Goals
  • Near Term
  • Rigid-Body Dynamics with 3 Degrees of Freedom
    (2D)?
  • Calculation of Accurate Pressures/Forces on
    Boundaries
  • Long Term
  • Deformable-Body Dynamics with 6 Degrees of
    Freedom
  • Non-uniform Time-stepping
  • Dynamic Particle Refinement
  • Parallelization Integration with OpenFOAM

3
Code Status
  • 2D Rigid Body Dynamics In Progress
  • Surface Pressures/Forces In Progress
  • Deformable Body Support ---
  • Particle Refinement Control ---
  • Non-Uniform Time-stepping ---
  • 3D/6DOF ---
  • Parallelization Integration w/ OpenFOAM ---

4
Theory - SPH Basics
  • Meshfree CFD Method
  • Particle Discretization of Continuous Fluid
  • Lagrangian Perspective
  • SPH Approximation of Fluid Field Calculations

Cubic Spline Kernel Function (Liu, Liu)?
SPH Form of N-S Governing Equations
5
Theory - SPH Basics (2)?
  • Integration over Support Domain Determines
    Fluid-Particle Properties
  • Equation of State Used to Determine Pressure

Summation-Density Formulation and Tait Equation
Support Domain (Liu, Liu)?
6
Program Structure
  • Domain Particles Stored in Quadtree Data
    Structure
  • Allows For Efficient Particle Support Domain
    Searching

Quadtree (Wikimedia Commons)?
7
Boundaries
  • Pressure Based Forces Depend on dW/dr
  • dW/dr approaches zero as r 0
  • Surface Penetration Prevention
  • Virtual Particles
  • Inverse-Square Repulsive Boundary Force
  • Line-Boundary

8
Surface Pressures/Forces
  • Current Code Estimates Forces/Pressures from
    Repulsion Force Only
  • Fails to take into account momentum transfer from
    virtual particle interactions with fluid
    particles
  • Desired Corrected Smoothed Particle Method
    (CSPM)?
  • Provides Accurate Density/Pressure Calculations
    Even at Boundaries

Truncated Support Domain (Liu, Liu)?
9
Example Simulations Cylinder Drop
10
Example Simulations Dam Break
11
Example Simulations Airfoil
12
Future Work Deformable Structures
  • Soft-Couple Object Particles to Underlying
    Physics Model (Skeleton)
  • i.e. Simple 3DOF Beam Element
  • Forces From Particles Transferred to Skeleton
  • Skeleton Deformations Modify Particle Positions

13
Future Work Non-uniform Timestep
  • Fractional time-stepping in regions of
    high-resolution particles provides a more uniform
    CFL number
  • Largest timesteps evaluated first, then
    positions/states are interpolated for adjacent
    particle timesteps
  • Investigate possibility of continuous timestep
    variation (as opposed to fractional)

14
Future Work Dynamic Particle Refinement
  • Merge/Split particles to maintain volumes of
    increased/decreased particle resolution
  • Investigate possibility of continuous particle
    refinement (vs. discreet merge/split) by particle
    to particle mass transport with spatial
    correction

15
References
  • Liu, Liu Smoothed Particle Hydrodynamics a
    meshfree particle method
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