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From: John Peterson <peterson@cf...>  20080122 23:14:17

David Knezevic writes: > I'd like to implement the following boundary condition for the outflow > of a channel: > du/dn  n*p = 0, > where n is the outward normal and p is the pressure. It seems to me that > this BC would result in an extra boundary term $\int_{\partial\Omega} n > p \ds$ being added to the momentum equations? Isn't this the natural boundary condition, assuming you integrated by parts on the pressure term? In that case I don't think you get any extra terms. J > In my case the outward normal on the outflow boundary is n = (1,0). I > tried to implement this BC using the following code in side_constraint: > > if (boundary_id == outflow_id) > Fu(i) = JxW_side[qp] * p * phi_side[i][qp]; > > if (boundary_id != outflow_id) > Fv(i) += JxW_side[qp] * penalty * > (v  v_value) * phi_side[i][qp]; > > if (boundary_id != outflow_id) > Kuu(i,j) += JxW_side[qp] * penalty * > phi_side[i][qp] * phi_side[j][qp]; > if (boundary_id != outflow_id) > Kvv(i,j) += JxW_side[qp] * penalty * > phi_side[i][qp] * phi_side[j][qp]; > > where p = side_value(p_var, qp), plus there are other BCs not shown > here for inflow and noslip. This doesn't appear to work; the Newton > convergence fails with these BCs. If anyone can point out how to > properly implement this BC, I'd be most appreciative :) > > Cheers, > David 
From: Roy Stogner <roystgnr@ic...>  20080122 23:02:58

On Tue, 22 Jan 2008, David Knezevic wrote: > I'd like to implement the following boundary condition for the outflow > of a channel: > du/dn  n*p = 0, > where n is the outward normal and p is the pressure. It seems to me that > this BC would result in an extra boundary term $\int_{\partial\Omega} n > p \ds$ being added to the momentum equations? That seems right. > In my case the outward normal on the outflow boundary is n = (1,0). I > tried to implement this BC using the following code in side_constraint: > > if (boundary_id == outflow_id) > Fu(i) = JxW_side[qp] * p * phi_side[i][qp]; > > if (boundary_id != outflow_id) > Fv(i) += JxW_side[qp] * penalty * > (v  v_value) * phi_side[i][qp]; > > if (boundary_id != outflow_id) > Kuu(i,j) += JxW_side[qp] * penalty * > phi_side[i][qp] * phi_side[j][qp]; > if (boundary_id != outflow_id) > Kvv(i,j) += JxW_side[qp] * penalty * > phi_side[i][qp] * phi_side[j][qp]; > > where p = side_value(p_var, qp), plus there are other BCs not shown > here for inflow and noslip. This doesn't appear to work; the Newton > convergence fails with these BCs. If anyone can point out how to > properly implement this BC, I'd be most appreciative :) For the new Fu term, you'll need a corresponding Jacobian term. Try: if (boundary_id == outflow_id) Kup(i,j) = JxW_side[qp] * psi_side[j][qp] * phi_side[i][qp];  Roy 
From: David Knezevic <dave.knez@gm...>  20080122 23:02:16

> It seems to me that this BC would result in an extra boundary term $\int_{\partial\Omega} n > p \ds$ being added to the momentum equations? > oops, I meant $\int_{\partial\Omega} n p \phi \ds$  David 
From: David Knezevic <david.knezevic@ba...>  20080122 22:53:32

I'd like to implement the following boundary condition for the outflow of a channel: du/dn  n*p = 0, where n is the outward normal and p is the pressure. It seems to me that this BC would result in an extra boundary term $\int_{\partial\Omega} n p \ds$ being added to the momentum equations? In my case the outward normal on the outflow boundary is n = (1,0). I tried to implement this BC using the following code in side_constraint: if (boundary_id == outflow_id) Fu(i) = JxW_side[qp] * p * phi_side[i][qp]; if (boundary_id != outflow_id) Fv(i) += JxW_side[qp] * penalty * (v  v_value) * phi_side[i][qp]; if (boundary_id != outflow_id) Kuu(i,j) += JxW_side[qp] * penalty * phi_side[i][qp] * phi_side[j][qp]; if (boundary_id != outflow_id) Kvv(i,j) += JxW_side[qp] * penalty * phi_side[i][qp] * phi_side[j][qp]; where p = side_value(p_var, qp), plus there are other BCs not shown here for inflow and noslip. This doesn't appear to work; the Newton convergence fails with these BCs. If anyone can point out how to properly implement this BC, I'd be most appreciative :) Cheers, David 
From: John Peterson <peterson@cf...>  20080122 22:20:50

Speak of the devil. I will try to attend this talk next month, though it looks like it will focus on more exotic FE spaces... J Sue Hennigar writes: > ICES SEMINAR > > Prof. Nilima Nigam > Department of Mathematics and Statistics > McGill University > "Highorder Conforming Finite Elements for a Pyramid" > > Abstract: > Pyramidal elements can arise in hybrid meshes as "gluing" elements > between hexahedral and tetrahedral structures. A longoutstanding > problem has been how to design highorder conforming finite elements on > the pyramid, which are compatible on their faces and edges with existing > elements from neighbouring tetrahedra or hexahedra. In this joint with > Joel Phillips, we present highorder elements, which satisfy the exact > sequence property for H1, H(curl), H(div) and L2, and which also have > the required compatibility features. Projectionbased interpolation > provides a natural strategy for the > construction, and also allows for a commuting diagram property. Along > the way, we describe the (surprising) result that such finite elements > cannot comprise of polynomial functions alone. > > February 7, 2008 > 3:30  5:00 pm > ACES 6.304 
From: John Peterson <peterson@cf...>  20080122 20:02:46

Michael Povolotskyi writes: > Dear Libmesh developers, at some point it appears such a comment in > the code (see below). Does it mean that the results obtained on a > mesh that contains pyramids may be wrong? Or they are for sure wrong? Hi, I was the one to add that comment. I didn't investigate the issue further, unfortunately. You can try it out yourself with a pyramid of known volume... Either the geometric volume formula we have is wrong or there is a problem with the quadrature rule or basis functions. If you take a look at the pyramid's basis functions, you will notice they are rational functions, not polynomials. John 
From: Michael Povolotskyi <povolotskyi@in...>  20080122 19:08:26

<!DOCTYPE html PUBLIC "//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> </head> <body bgcolor="#ffffff" text="#000000"> <pre class="fragment">Dear Libmesh developers, at some point it appears such a comment in the code (see below). Does it mean that the results obtained on a mesh that contains pyramids may be wrong? Or they are for sure wrong? Thank you, Michael. <a class="code" href="http://libmesh.sourceforge.net/doxygen/libmesh__common_8h.php#cd9440203db8e3b36d61f62fe6567258">Real</a>; <a class="code" href="http://libmesh.sourceforge.net/doxygen/classPyramid5.php#c92644b060057bd04f860055ba2c7014">Pyramid5::volume</a>; ()<span class="keyword"> const</span> <span class="comment"></span> 00266 <span class="comment">// Note: the volume returned by summing the Jacobian times the</span> 00267 <span class="comment">// quadrature weights over all the quadrature points for the</span> 00268 <span class="comment">// pyramid element does *not* give the correct volume (the formula</span> 00269 <span class="comment">// in this function gives the correct volume). This implies there</span> 00270 <span class="comment">// is something wrong with the firstorder Lagrange shape functions</span> 00271 <span class="comment">// or the quadrature rules for the Pyramid5.</span></pre> <pre class="mozsignature" cols="72"> </pre> </body> </html> 