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ALCF Science 1 - Argonne National Laboratory

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argonne leadership computing facility<br />

Materials <strong>Science</strong><br />

Large-Scale Condensed Matter and Fluid Dynamics Simulations<br />

Identifying UPOs in the Navier-Stokes Equations with HYPO4D<br />

University College London researchers are applying dynamical systems<br />

theory to three-dimensional fluid turbulence. They are taking a novel<br />

space-time variational approach using the HYPO4D code and have<br />

located several Unstable Periodic Orbits (UPOs). The main advantage of<br />

storing UPOs to represent a turbulent flow is that it needs to be done<br />

only once. In the future, the turbulent average of any given quantity<br />

can be computed directly from the UPO library with high accuracy and<br />

without the need to solve an initial value problem, using the dynamical<br />

zeta function formulation. This methodology has the potential to<br />

become a new paradigm in the study of large, driven dissipative<br />

dynamical systems, not only for the Navier-Stokes equations.<br />

INCITE Allocation:<br />

40 Million Hours<br />

INCITE PROGRAM<br />

35<br />

Snapshots of the vorticity field of a UPO located<br />

in weakly turbulent flow with Re=371 and period<br />

equal to 26864 LB time steps. The quantity shown<br />

is the magnitude of vorticity above a given cut-off<br />

level. Red corresponds to large negative vorticity<br />

(clockwise rotation), and blue to large positive<br />

vorticity (counter-clockwise rotation).<br />

Contact Peter Coveney<br />

University College London | p.v.coveney@ucl.ac.uk

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