286 research outputs found
Dynamic Unstructured Method for Prescribed and Aerodynamically Determined Relative Moving Boundary Problems
A new methodology is developed to simulate unsteady flows about prescribed and aerodynamically determined moving boundary problems. The method couples the fluid dynamics and rigid-body dynamics equations to capture the time-dependent interference between stationary and moving boundaries. The unsteady, compressible, inviscid (Euler) equations are solved on dynamic, unstructured grids by an explicit, finite-volume, upwind method. For efficiency, the grid adaptation is performed within a window around the moving object. The Eulerian equations of the rigid-body dynamics are solved by a Runge-Kutta method in a non-inertial frame of reference. The two-dimensional flow solver is validated by computing the flow past a sinusoidally-pitching airfoil and comparing these results with the experimental data. The overall methodology is used for two two-dimensional examples: the flow past an airfoil which is performing a three-degrees-of-freedom motion in a transonic freestream, and the free-fall of a store after separation from a wing-section. Then the unstructured mesh methodology is extended to three-dimensions to simulate unsteady flow past bodies in relative motion, where the trajectory is determined from the instantaneous aerodynamics. The flow solver and the adaptation scheme in three-dimensions are validated by simulating the transonic, unsteady flow around a wing undergoing a forced, periodic, pitching motion, and comparing the results with the experimental data. To validate the trajectory code, the six-degrees-of-freedom motion of a store separating from a wing was computed using the experimentally determined force and moment fields, then comparing with an independently generated trajectory. Finally, the overall methodology was demonstrated by simulating the unsteady flowfield and the trajectory of a store dropped from a wing. The methodology, its computational cost notwithstanding, has proven to be accurate, automated, easy for dynamic gridding, and relatively efficient for the required man-hours
EQUIVARIANT STABLE HOMOTOPY THEORY FOR PROPER ACTIONS OF DISCRETE GROUPS
Following ideas of Graeme Segal [Segal(1973)], [Segal(1968)],
Christian Schlichtkrull [Schlichtkrull(2007)] and Kazuhisa Shimakawa
[Shimakawa(1989)] we construct equivariant stable homotopy groups for
proper equivariant CW complexes with an action of a discrete group
A development of grid generation procedure for multicomponent aerodynamic configuration
Two approaches for solving the transonic flow in a multi-block grid were explored. The first approach examines a method involving "zonal decomposition" wherein block boundaries are treated as true boundary surfaces separating interfacing grids. The issues investigated involve techniques for matching solutions at a block boundary. A feasibility study was completed and the results are presented. The second approach involves overlapping grids for differencing across a block boundary near an artificially induced coordinate singularity occurring at a fictitious corner. This approach selects a set of neighboring nodes for the fictitious corner such that the resulting physical cells for a node are topologically the same as any other node on the airfoil surface
Gale duality and Koszul duality
Given an affine hyperplane arrangement with some additional structure, we
define two finite-dimensional, noncommutative algebras, both of which are
motivated by the geometry of hypertoric varieties. We show that these algebras
are Koszul dual to each other, and that the roles of the two algebras are
reversed by Gale duality. We also study the centers and representation
categories of our algebras, which are in many ways analogous to integral blocks
of category O.Comment: 55 pages; v2 contains significant revisions to proofs and to some of
the results. Section 7 has been deleted; that material will be incorporated
into a later paper by the same author
Manifold-based isogeometric analysis basis functions with prescribed sharp features
We introduce manifold-based basis functions for isogeometric analysis of
surfaces with arbitrary smoothness, prescribed continuous creases and
boundaries. The utility of the manifold-based surface construction techniques
in isogeometric analysis was demonstrated in Majeed and Cirak (CMAME, 2017).
The respective basis functions are derived by combining differential-geometric
manifold techniques with conformal parametrisations and the partition of unity
method. The connectivity of a given unstructured quadrilateral control mesh in
is used to define a set of overlapping charts. Each vertex with
its attached elements is assigned a corresponding conformally parametrised
planar chart domain in , so that a quadrilateral element is
present on four different charts. On the collection of unconnected chart
domains, the partition of unity method is used for approximation. The
transition functions required for navigating between the chart domains are
composed out of conformal maps. The necessary smooth partition of unity, or
blending, functions for the charts are assembled from tensor-product B-spline
pieces and require in contrast to earlier constructions no normalisation.
Creases are introduced across user tagged edges of the control mesh. Planar
chart domains that include creased edges or are adjacent to the domain boundary
require special local polynomial approximants. Three different types of chart
domain geometries are necessary to consider boundaries and arbitrary number and
arrangement of creases. The new chart domain geometries are chosen so that it
becomes trivial to establish local polynomial approximants that are always
continuous across tagged edges. The derived non-rational manifold-based
basis functions are particularly well suited for isogeometric analysis of
Kirchhoff-Love thin shells with kinks
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