2,450 research outputs found
A conservative coupling algorithm between a compressible flow and a rigid body using an Embedded Boundary method
This paper deals with a new solid-fluid coupling algorithm between a rigid
body and an unsteady compressible fluid flow, using an Embedded Boundary
method. The coupling with a rigid body is a first step towards the coupling
with a Discrete Element method. The flow is computed using a Finite Volume
approach on a Cartesian grid. The expression of numerical fluxes does not
affect the general coupling algorithm and we use a one-step high-order scheme
proposed by Daru and Tenaud [Daru V,Tenaud C., J. Comput. Phys. 2004]. The
Embedded Boundary method is used to integrate the presence of a solid boundary
in the fluid. The coupling algorithm is totally explicit and ensures exact mass
conservation and a balance of momentum and energy between the fluid and the
solid. It is shown that the scheme preserves uniform movement of both fluid and
solid and introduces no numerical boundary roughness. The effciency of the
method is demonstrated on challenging one- and two-dimensional benchmarks
Multiscale Turbulence Models Based on Convected Fluid Microstructure
The Euler-Poincar\'e approach to complex fluids is used to derive multiscale
equations for computationally modelling Euler flows as a basis for modelling
turbulence. The model is based on a \emph{kinematic sweeping ansatz} (KSA)
which assumes that the mean fluid flow serves as a Lagrangian frame of motion
for the fluctuation dynamics. Thus, we regard the motion of a fluid parcel on
the computationally resolvable length scales as a moving Lagrange coordinate
for the fluctuating (zero-mean) motion of fluid parcels at the unresolved
scales. Even in the simplest 2-scale version on which we concentrate here, the
contributions of the fluctuating motion under the KSA to the mean motion yields
a system of equations that extends known results and appears to be suitable for
modelling nonlinear backscatter (energy transfer from smaller to larger scales)
in turbulence using multiscale methods.Comment: 1st version, comments welcome! 23 pages, no figures. In honor of
Peter Constantin's 60th birthda
Evaluating the boundary and covering degree of planar Minkowski sums and other geometrical convolutions
AbstractAlgorithms are developed, based on topological principles, to evaluate the boundary and “internal structure” of the Minkowski sum of two planar curves. A graph isotopic to the envelope curve is constructed by computing its characteristic points. The edges of this graph are in one-to-one correspondence with a set of monotone envelope segments. A simple formula allows a degree to be assigned to each face defined by the graph, indicating the number of times its points are covered by the Minkowski sum. The boundary can then be identified with the set of edges that separate faces of zero and non-zero degree, and the boundary segments corresponding to these edges can be approximated to any desired geometrical accuracy. For applications that require only the Minkowski sum boundary, the algorithm minimizes geometrical computations on the “internal” envelope edges, that do not contribute to the final boundary. In other applications, this internal structure is of interest, and the algorithm provides comprehensive information on the covering degree for different regions within the Minkowski sum. Extensions of the algorithm to the computation of Minkowski sums in R3, and other forms of geometrical convolution, are briefly discussed
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