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Subject: fundamental solution ×

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Now showing 1 - 3 of 3
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    On the spatially asymptotic structure of time-periodic solutions to the Navier--Stokes equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Eiter, Thomas
    The asymptotic behavior of weak time-periodic solutions to the Navier--Stokes equations with a drift term in the three-dimensional whole space is investigated. The velocity field is decomposed into a time-independent and a remaining part, and separate asymptotic expansions are derived for both parts and their gradients. One observes that the behavior at spatial infinity is determined by the corresponding Oseen fundamental solutions.
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    Spatial decay of the vorticity field of time-periodic viscous flow past a body
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Eiter, Thomas; Galdi, Giovanni P.
    We study the asymptotic spatial behavior of the vorticity field associated to a time-periodic Navier-Stokes flow past a body in the class of weak solutions satisfying a Serrin-like condition. We show that outside the wake region the vorticity field decays pointwise at an exponential rate, uniformly in time. Moreover, decomposing it into its time-average over a period and a so-called purely periodic part, we prove that inside the wake region, the time-average has the same algebraic decay as that known for the associated steady-state problem, whereas the purely periodic part decays even faster, uniformly in time. This implies, in particular, that ``sufficiently far'' from the body, the time-periodic vorticity field behaves like the vorticity field of the corresponding steady-state problem.
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    On a fast integral equation method for diffraction gratings
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Rathsfeld, Andreas; Schmidt, Gunther; Kleemann, Bernd
    The integral equation method for the simulation of the diffraction by optical gratings is an efficient numerical tool if profile gratings determined by simple cross-section curves are considered. This method in its recent version is capable to tackle profile curves with corners, gratings with thin coated layers, and diffraction scenarios with unfavorably large ratios period over wavelength. We discuss special implementational issues including the efficient evaluation of the quasi-periodic Green kernels, the quadrature algorithm, and the iterative solution of the arising systems of linear equations. Finally, as application we present the simulation of coated echelle gratings which demonstrates the efficency of our approach.