Interdisciplinary Applied Mathematics

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In Figure 14.18 we plot the streamwise (left figure) and wall-normal (right figure) velocity profiles at three downstream locations, x = 0, R, and 2R, computed with all three methods. All three methods agree with one another quite well in the region far away from the sphere (x = 2R). Closer to the sphere surface and inside the sphere, the spectral DLM results are in good agreement with DNS results, while larger discrepancies between FCM and DNS results are observed in these regions. Due to asymmetry in the configuration, the flow exerts a torque and a lift force on the sphere. The coefficients for the drag and lift forces on the sphere and the torque with respect to the z-axis computed with all three methods are summarized in    Table 14.4.    FCM    overpredicts    the    drag    force    on    the sphere    by    about


6%. However, given the small number of elements, FCM simulations have produced lift and torque values that are in quite good agreement with DNS. FCM is a very fast method and scales favorably for a large number of particles.    Even    in    this application    with    a single    sphere,    FCM    was    one


to two    orders    of magnitude    faster    than DNS    or    DLM;    the    latter    was    as


expensive as DNS. The drag and lift forces produced by spectral DLM are in good agreement with DNS results; the errors are within 2%. It is noted that poorly    resolved    regions    on    the    surface    of    the    sphere could    affect the


accuracy of the torque in DLM. For example, if the boundary collocation points consist only of intersection points between the sphere surface and the


Elements/Grid DNS 4608(5th order) 4608(7th order) 4608(8th order) FCM    360(4th order)


36o(6th order) 360(8th order) DLM 96 x 60 x 96 96 x 72 x 96 96    84    96



Cd


Cl

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