SPH research at National University of Ireland, Galway Nathan Quinlan, Marty Lastiwka, Mihai Basa 10 October, 2005

SPH SIG, 10 October 2005 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 Biomedical flows Moving geometries (artery walls, heart valves) Complex, unique geometries from 3D and “4D” medical imaging

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

SPH SIG, 10 October 2005 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 Truncation error analysis of SPH in 1D discretisatio n error smoothing error x j = particle location  x j = particle volume x j = centre of particle volume A(x) = data function

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

SPH SIG, 10 October 2005 The need for adaptive SPH flow inlet outlet shock

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

SPH SIG, 10 October 2005 Results – adaptive particle distribution

SPH SIG, 10 October 2005 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) Evaluation of second derivatives for viscous flow

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

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

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

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