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Smoothed Particle Hydrodynamics For Deformable Vessel Dynamics

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

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Smoothed Particle Hydrodynamics For Deformable Vessel Dynamics

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

  2. 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 Research Goals

  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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