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SPH research at National University of Ireland, Galway

SPH research at National University of Ireland, Galway. Nathan Quinlan, Marty Lastiwka, Mihai Basa 10 October, 2005. Biomedical flows Moving geometries (artery walls, heart valves) Complex, unique geometries from 3D and “4D” medical imaging. Background and Motivation.

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SPH research at National University of Ireland, Galway

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  1. SPH researchat National University of Ireland, Galway Nathan Quinlan, Marty Lastiwka, Mihai Basa 10 October, 2005

  2. Biomedical flows Moving geometries (artery walls, heart valves) Complex, unique geometries from 3D and “4D” medical imaging Background and Motivation Making CFD more accessible Can we do without mesh generation? Began working on SPH in 2001 Funding awarded by Irish Research Council for Science, Engineering and Technology for 4-year project starting 2003 SPH SIG, 10 October 2005

  3. Activities to date • Theoretical study of accuracy • Adaptive particle distribution • Viscous flow • Incompressible flow SPH SIG, 10 October 2005

  4. Accuracy of SPH SPH does not exactly reproduce a constant-valued function – it is not zero-order consistent Consistency-corrected SPH methods (like RKPM) guarantee exact reproduction of polynomials of order 0, 1, … SPH SIG, 10 October 2005

  5. xj = centre of particle volume Truncation error analysis of SPH in 1D smoothing error discretisation error xj = particle location Dxj = particle volume A(x) = data function SPH SIG, 10 October 2005

  6. corrected kernel Numerical experiments in 3D standard kernel SPH SIG, 10 October 2005

  7. shock particles inserted at inlet The need for adaptive SPH flow inlet outlet SPH SIG, 10 October 2005

  8. y x Location of discontinuity at t=0 z Test case: quasi-3D shock tube flow instantaneous density field flow SPH SIG, 10 October 2005

  9. Results – adaptive particle distribution SPH SIG, 10 October 2005

  10. Evaluation of second derivatives for viscous flow Method 1: mixed finite-difference / SPH Monaghan (1992), Morris et al. (1996) Method 2: Direct second derivatives of kernel Successfully used by Takeda et al. (1994), with Gaussian kernels. Method 3: Two passes of standard SPH with W Introduced by Flebbe et al. (1994) and Watkins et al. (1996) SPH SIG, 10 October 2005

  11. 2-pass Evaluation of second derivatives for viscous flow finite difference / SPH SPH SIG, 10 October 2005

  12. Incompressible flow Similar to pressure projection technique of Cummins and Rudman New method based on Clebsch-Weber decomposition SPH SIG, 10 October 2005

  13. Incompressible flow .u, normalised time step SPH SIG, 10 October 2005

  14. Current and future work • Boundary conditions • Turbulence modelling • Parallelisation • Application to mechanical heart valves SPH SIG, 10 October 2005

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