<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"> https://aip.scitation.org/doi/pdf/10.1063/1.4994603</a> for details regarding the filtering operation.<br></div></div><div class="gmail_extra"><br><div class="gmail_quote">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.gov</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><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_-431713167691286608_Xbe">1 Rue de la Noë, 44321 Nantes, France<br></span></div></div></div></div><br>______________________________<wbr>_________________<br>
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