<div dir="ltr">Hello,<div><br></div><div>The Stokes flow equations are a 3d version of the equations attached (Stokes-Leslie Flow). Only variables/unknowns are v and u_xy=0.5(Dx(vy)+Dy(vx).</div><div><br></div><div>I am trying to solve them iteratively by correcting the pressure to reach a steady state. I start with 0 pressure. Currently, I am unable to solve the first iteration (periodic in X and Z. V=0 at Y=0 and Dx(vy)+Dy(vx)=g(x) at Y=10).</div><div><br></div><div>I think the equations might be singular but I am not sure as in my experience, the problem is well posed if the solution is known at certain boundaries.</div><div><br></div><div><br></div><div><img src="cid:ii_knoxluuv0" alt="by default 2021-04-19 at 20.28.28.png" width="562" height="345"><br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Mon, 19 Apr 2021 at 15:59, Matthew Knepley <<a href="mailto:knepley@gmail.com">knepley@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div dir="ltr">On Mon, Apr 19, 2021 at 9:37 AM Abhinav Singh <<a href="mailto:abhinavrajendra@gmail.com" target="_blank">abhinavrajendra@gmail.com</a>> wrote:<br></div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">What does this mean? Stokes means using an incompressibility constraint, for which we often introduce a pressure.</blockquote><div>Yes, what I mean is solving the momentum block, say with known pressure. viscosity is constant however, the momentum equation has both Laplacian and Gradient terms.</div></div></blockquote><div><br></div><div>That does not make any sense to me. Can you write the equation?</div><div><br></div><div> Thanks,</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">You should use a good Laplacian preconditioner, like -pc_type gamg or -pc_type ml.</blockquote><div>I tried gamg and it seems to diverge as the solution is NaN. The KSP residual message is "<span style="font-variant-ligatures:no-common-ligatures;background-color:rgba(0,0,0,0.9);color:rgb(47,255,18);font-family:"Source Code Pro";font-size:18px"> </span><span style="font-variant-ligatures:no-common-ligatures;background-color:rgba(0,0,0,0.9);color:rgb(47,255,18);font-family:"Source Code Pro";font-size:18px">0 KSP Residual norm 1.131782747169e+01</span><span style="font-variant-ligatures:no-common-ligatures;background-color:rgba(0,0,0,0.9);color:rgb(47,255,18);font-family:"Source Code Pro";font-size:18px"> </span> ".</div><div>When using -pc_type ml, I get Aggregate Warning and then some faulty address which stops the code.</div><div><br></div>
<div><br></div></div><div></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Mon, 19 Apr 2021 at 12:31, Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div dir="ltr">On Mon, Apr 19, 2021 at 6:18 AM Abhinav Singh <<a href="mailto:abhinavrajendra@gmail.com" target="_blank">abhinavrajendra@gmail.com</a>> wrote:<br></div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr">Hello all,<div><br></div><div>I am trying to solve for incompressible stokes flow on a particle based discretization. I use a pressure correction technique along with Particle strength exchange like operators. </div><div><br></div><div>I call Petsc to solve the Stokes Equation without the pressure term. </div></div></blockquote><div><br></div><div>What does this mean? Stokes means using an incompressibility constraint, for which we often introduce a pressure.</div><div><br></div><div>Do you mean you are solving only the momentum block? If so, do you have a constant viscosity? If so, then this is just the Laplace equation.</div><div>You should use a good Laplacian preconditioner, like -pc_type gamg or -pc_type ml.</div><div><br></div><div> Thanks</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div>GMRES usually works great but with dirichlet boundary conditions. When I use a mixed boundary condition in Y, (dirichlet on bottom and Neumann on the top) with periodicity in X,Z. GMRES fails converge when the size of matrix increases. For smaller size (upto 27*27*5), only GMRES works and that too only with the option 'pc_type none'. I was unable to find any preconditioner which worked. Eventually, it also fails for bigger size. UMFPACK works but LU decomposition fails after a certain size and is very slow.</div><div><br></div><div>It would be great if you could suggest a way or a preconditioner which suits this problem.</div><div><br></div><div>Kind regards,</div><div>Abhinav </div></div>
</blockquote></div><br clear="all"><div><br></div>-- <br><div dir="ltr"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener</div><div><br></div><div><a href="http://www.cse.buffalo.edu/~knepley/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br></div></div></div></div></div></div></div></div>
</blockquote></div>
</blockquote></div><br clear="all"><div><br></div>-- <br><div dir="ltr"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener</div><div><br></div><div><a href="http://www.cse.buffalo.edu/~knepley/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br></div></div></div></div></div></div></div></div>
</blockquote></div>