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M. Oliver and O. Bühler,
Transparent boundary conditions as dissipative subgrid closures for
the spectral representation of scalar advection by shear flows,
J. Math. Phys. 48 (2007), 065502, 26 pp.
Abstract:
We consider the evolution of a passive scalar in a shear flow in its
representation as a system of lattice differential equations in wave
number space. When the velocity field has small support, the
interaction in wave number space is local and can be studied in terms
of dispersive linear lattice waves. We close the restriction of the
system to a finite set of wave numbers by implementing transparent
boundary conditions for lattice waves. This closure is studied
numerically in terms of energy dissipation rate and energy spectrum,
both for a time-independent velocity field and for a time-dependent
synthetic velocity field whose Fourier coefficients follow independent
Ornstein-Uhlenbeck stochastic processes.
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