14,106 research outputs found
On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high Reynolds number flow over an Ahmed body
We investigate a hierarchy of eddy-viscosity terms in POD Galerkin models to
account for a large fraction of unresolved fluctuation energy. These Galerkin
methods are applied to Large Eddy Simulation data for a flow around the
vehicle-like bluff body call Ahmed body. This flow has three challenges for any
reduced-order model: a high Reynolds number, coherent structures with broadband
frequency dynamics, and meta-stable asymmetric base flow states. The Galerkin
models are found to be most accurate with modal eddy viscosities as proposed by
Rempfer & Fasel (1994). Robustness of the model solution with respect to
initial conditions, eddy viscosity values and model order is only achieved for
state-dependent eddy viscosities as proposed by Noack, Morzynski & Tadmor
(2011). Only the POD system with state-dependent modal eddy viscosities can
address all challenges of the flow characteristics. All parameters are
analytically derived from the Navier-Stokes based balance equations with the
available data. We arrive at simple general guidelines for robust and accurate
POD models which can be expected to hold for a large class of turbulent flows.Comment: Submitted to the Journal of Fluid Mechanic
Explicit parametric solutions of lattice structures with proper generalized decomposition (PGD): applications to the design of 3D-printed architectured materials
The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-017-1534-9Architectured materials (or metamaterials) are constituted by a unit-cell with a complex structural design repeated periodically forming a bulk material with emergent mechanical properties. One may obtain specific macro-scale (or bulk) properties in the resulting architectured material by properly designing the unit-cell. Typically, this is stated as an optimal design problem in which the parameters describing the shape and mechanical properties of the unit-cell are selected in order to produce the desired bulk characteristics. This is especially pertinent due to the ease manufacturing of these complex structures with 3D printers. The proper generalized decomposition provides explicit parametic solutions of parametric PDEs. Here, the same ideas are used to obtain parametric solutions of the algebraic equations arising from lattice structural models. Once the explicit parametric solution is available, the optimal design problem is a simple post-process. The same strategy is applied in the numerical illustrations, first to a unit-cell (and then homogenized with periodicity conditions), and in a second phase to the complete structure of a lattice material specimen.Peer ReviewedPostprint (author's final draft
Modal decomposition of astronomical images with application to shapelets
The decomposition of an image into a linear combination of digitised basis
functions is an everyday task in astronomy. A general method is presented for
performing such a decomposition optimally into an arbitrary set of digitised
basis functions, which may be linearly dependent, non-orthogonal and
incomplete. It is shown that such circumstances may result even from the
digitisation of continuous basis functions that are orthogonal and complete. In
particular, digitised shapelet basis functions are investigated and are shown
to suffer from such difficulties. As a result the standard method of performing
shapelet analysis produces unnecessarily inaccurate decompositions. The optimal
method presented here is shown to yield more accurate decompositions in all
cases.Comment: 12 pages, 17 figures, submitted to MNRA
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