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A flexibly mounted circular cylinder in cross-flow, with natural frequencies in the inline and transverse directions having a ratio close to 2:1, exhibits drastic changes in the vortex structures in its wake, the frequency content of the fluid forces, and the orbital shape of its resulting motions. Stable multivortex patterns form in the cylinder wake, associated with large high-frequency force components.

We present a new algorithm based on Wiener-Hermite functionals combined with Fourier collocation to solve the advection equation with stochastic transport velocity. We develop different stategies of representing the stochastic input, and demonstrate that this approach is orders of magnitude more efficient than Monte Carlo simulations for comparable accuracy. Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

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1. Full-scale simulations of the virtual physiological human (VPH) will require significant advances in modelling, multiscale mathematics, scientific computing and further advances in medical imaging. Herein, we review some of the main issues that need to be resolved in order to make three-dimensional (3D) simulations of blood flow in the human arterial tree feasible in the near future. 2. A straightforward approach is computationally prohibitive even on the emerging petaflop supercomputers, so a three-level hierarchical approach based on vessel size is required, consisting of: (i) a macrovascular network (MaN); (ii) a mesovascular network (MeN); and (iii) a microvascular network (MiN). We present recent simulations of MaN obtained by solving the 3D Navier-Stokes equations on arterial networks with tens of arteries and bifurcations and accounting for the neglected dynamics through proper boundary conditions. 3. A multiscale simulation coupling MaN-MeN-MiN and running on hundreds of thousands of processors on petaflop computers will require no more than a few CPU hours per cardiac cycle within the next 5 years. The rapidly growing capacity of supercomputing centres opens up the possibility of simulation studies of cardiovascular diseases, drug delivery, perfusion in the brain and other pathologies.

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