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Michel A.T. Hinsberg (TU/e - TN)
| Speaker: |
Michel A.T. van Hinsberg
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| Date: |
Wednesday March 30, 2011
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| Title: |
Computational
methods
for particle tracking in isotropic turbulence
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Abstract
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The
hydrodynamic
force exerted by a fluid on small isolated rigid spherical
particles are usually well described by the Maxey-Riley (MR) equations.
In order to be able to simulate a large number of particles the methods
for solving the MR equations need to be fast and accurate. The most
time-consuming contribution in the MR equations is the Basset history
force which is a well-known problem for many-particle simulations in
turbulence. In this study a novel numerical approach is proposed for
the computation of the Basset history force based on the use of
exponential functions to approximate the tail of the Basset force
kernel. Typically, this approach not only decreases the cpu time and
memory requirements for the Basset force computation by more than one
order of agnitude, but also increases the accuracy by an order of
magnitude. The method has a temporal accuracy of O(Δt2) which is a
substantial improvement compared to methods available in the
literature. Furthermore, the method is partially implicit in order to
increase stability of the computation.
Another important aspect in numerical simulations of particle laden
turbulent flows is the interpolation of the flow field. For the
interpolation many different approaches are used. Where some studies
use low order linear interpolation others use high order spline
methods. This study focuses on estimating the error made by the
interpolation method and compares it with the error made in the
discretisation of the flow field. In this way one can balance the
errors in order to achieve an optimal result. As a spin-off, a
practical method is proposed that enables direct estimation of the
interpolation error from the energy spectrum. Furthermore, it is shown
how the energy spectrum is changed due to the interpolation. Because
high order interpolation methods are computationally expensive, a
numerical method is proposed for fast computation.
A third part of the present study considers the Faxén
corrections which are first order corrections in the MR equations for
increasing particle radii. In most studies these corrections have been
implemented by using the Laplacian of the flow field. Recently it has
been shown that using volume and surface averages for the calculation
of the Faxén corrections give more reliable results for larger
particle radii. In this study a method is proposed that does the
averaging exactly in spectral space. Besides that our method is more
accurate it is also faster.
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