<div dir="ltr">PS: Additionally, to answer your question " <div><b><i>Lastly, removing high wave number parts of Legendre expansion seems
makes no sense physically. After all, the energy spectral of turbulence
is represented in Fourier series.<br></i></b></div><div><b><i>Does anyone has any idea on these puzzles</i></b>?"<br><br></div><div>-- Within each element, every variable is expanded as a function of Legendre polynomials. Note, that higher the order (mode) of the polynomial the more frequent oscillations it has. So in this sense, the highly frequent oscillations are somewhat very similar to the frequency/wavenumber in a classical Fourier series. A relation between mode and frequency would be worth a derivation, but the idea is just as a function can be thought of as a series of different frequency/wave number content sine/cosine oscillations, similarly an aperiodic function can be thought of as a series of Legendre polynomials of different modes. In this sense, removing/ filtering a highest modes of the transfer function, is equivalent to removing the high frequency content of the flow variables. It would have a similar effect in removing the high frequency content of a turbulent flow field.<br><br></div><div>HTH,<br><br></div><div>Tanmoy<br></div><br></div><div class="gmail_extra"><br><div class="gmail_quote">On Thu, Mar 15, 2018 at 10:58 AM, <span dir="ltr"><<a href="mailto:nek5000-users@lists.mcs.anl.gov" target="_blank">nek5000-users@lists.mcs.anl.gov</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><span class=""><div dir="ltr"><div>Hello Zhenrong,<br><br>fh is the 1D filter transformation matrix i.e. applied by kronecker product transformation for 3D. So, for 3D case, is u_ijk is the velocity data at each element, fh X fh X fh . u_ijk is the filtered variable, where X denotes the kronecker multiplication and . denotes the matrix multiplication. fht is the transpose of fh. You can look into the tens3d1() routine in postpro.f for more details.<br><br></div><div>If you denote fh as <b>F</b> in matrix notation, then<br><br></div><div><b>F</b> =<b> V D V^</b>-1, where <b>V </b>is the transformation matrix from nodal to modal (Legendre) space, and V ^-1, the inverse transformation. Now, D is the diagonal transfer function, which is referred to as diag in the routine. You can design your diag() in any way you want. diag is a nx X nx matrix, with non-zero diagonal. The first two entries of the diagonal needs to be 1, probably to maintain C0 continuity of u (I need to check that), and you can design the shape of the diagonal entries, in any way you want, (.i.e. as a function of cut-off modes.) You can look into the appendix of the paper<a href="https://aip.scitation.org/doi/pdf/10.1063/1.4994603" target="_blank"> https://aip.scitation.org/doi/<wbr>pdf/10.1063/1.4994603</a> for details regarding the filtering operation.<br></div></div></span><div class="gmail_extra"><br><div class="gmail_quote"><span class="">On Thu, Mar 15, 2018 at 6:20 AM, <span dir="ltr"><<a href="mailto:nek5000-users@lists.mcs.anl.gov" target="_blank">nek5000-users@lists.mcs.anl.<wbr>gov</a>></span> wrote:<br></span><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><div class="h5"><div><div style="font-family:arial,helvetica,sans-serif;font-size:12pt;color:#000000"><div>Hello everyone,<br></div><div><br></div><div>I have been working on the turbulent channel case for some time. But I am quite confused with the filtering technique in the turbChannel.usr. <br></div><div>I understand well the filtering technique for improving stability (p101 and p103), thanks to the discussion on the forum. However, is the same technique used in the build_1d_filt ? basically, partly removing the high wavenumber spectral in the expansion ?<br></div><div><br></div><div>I have a question about transfer function also:<br></div><div><br></div><div> diag(nx-0) = 0.05 <br> diag(nx-1) = 0.50<br> diag(nx-2) = 0.95<br></div><div><br></div><div>It seems to me that the diag(:) would determine how much energy will be removed for the high wave number spectral? but what are the variables fh, fht in the subroutine <br></div><div>build_1d_filt (fh,fht,diag,nx,nid) ?<br></div><div><br></div><div>it seems quite difficult to apply the more traditional filters like top-hat filter or Gaussian filter in the Nek5000. <br></div><div><br></div><div>Lastly, removing high wave number parts of Legendre expansion seems makes no sense physically. After all, the energy spectral of turbulence is represented in Fourier series.<br></div><div><br></div><div>Does anyone has any idea on these puzzles? Any discussion is greatly appreciated. <br></div><div><br></div><div>Best regards<br></div><div><br></div><div><div>Bien cordialement<br></div><div><br></div><div>Zhenrong JING<br></div><div><br></div><div>Doctorant (Doctor Candidate)<br></div><div><br></div><div>LHEEA</div><div><br></div><div>Ecole Centrale de Nantes<br></div><div><br></div><div><span class="m_4228584555726745868m_-431713167691286608_Xbe">1 Rue de la Noë, 44321 Nantes, France<br></span></div></div></div></div><br></div></div><span class="">______________________________<wbr>_________________<br>
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