<div class="gmail_quote">On Tue, Nov 15, 2011 at 12:03, Brandt Belson <span dir="ltr"><<a href="mailto:bbelson@princeton.edu">bbelson@princeton.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<div id=":xq">I'm not sure what you mean by the sign of the shift, but the equations are roughly of the form:<div><br></div><div>(I dt/Re - L) u = f</div><div><br></div><div>where dt~0.1, Re~1000, and L is the Laplacian in 3D,</div>
</div></blockquote><div><br></div><div>The time step size is in the numerator? (It's more commonly the other way.)</div><div><br></div><div>In any case, this is a positive shift, so you always have a positive definite operator. Multigrid should work very well, so you shouldn't need to bother with direct solvers.</div>
<div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"><div id=":xq"><div> so once it is Fourier transformed each x-y plane has equations like this:</div>
<div><br></div><div>(I dt/Re + I k_z^2 - L_{k_z}) \hat{u}_{k_z} = \hat{f}_{k_z}<br><br>I'm not sure which wavenumber you mean, but k_z goes as nz. </div></div></blockquote><div><br></div><div>It arises for frequency-domain problems where the shift is in the other direction (producing an indefinite operator). </div>
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