Dear Vikram,
Yes. I do agree with your remarks on the geometrical singularity, indeed.
Of course, refinement can remedy this to some extents. But from the
view of a practical large problem, between this weak implementation of
Dirichlet BC and the direct nodewise value assiging way, which is better?
May the latter way introduce other qeustions, such as convergence?
So this is my first question here.
At the same time, I compared the result discussed above with the results
from a Feel++ code with triangular meshes of roughly same mesh resolution
(gmsh.hsize=0.05). Here further weak terms are added for
symmetry of the Jacobian matrix, such as terms of
-\int_{Gamma_D} (\mu\nabla v-qI)\cdot\vec{n}\cdot (u-u_bc)
Since Feel++ encapsulated all details of BC implementation quite well, I can't
tell you how it works yet at the level of source codes.
I inserted these terms in my libmesh code as well. But The comparison
showed that the results did not match the accuracy of the Feel++ codes yet.
If you like, I can send it to you later.
Zhenyu
------------------ ???????? ------------------
??????: "Vikram Garg";<[email protected]>;
????????: 2015??3??19??(??????) ????0:59
??????: "grandrabbit"<[email protected]>;
????: "libmesh-users"<[email protected]>;
????: Re: [Libmesh-users] Proper way of imposing Weak Dirichlet boundary
condition
What happens if you refine the mesh ? The spurious oscillation you are seeing
could be because of the singularity at the corners where the boundary condition
is not well defined.
On Tue, Mar 17, 2015 at 7:59 PM, grandrabbit <[email protected]> wrote:
Thank you for your timely response.
I reset h_elem to 1.0. No big difference. In fact in this case the mesh is
uniform, with 20 cells along one dimension, h_elem is a constant, say, 1.25e-2.
Since I set penalty to 1.e+8, the actually penalty is 8.e9,
similar to intro_ex3. Therefore I think the true reason is located elsewhere .
BTW, is there any example for TransientNonlinearImplicitSystem? When I start
the coding, I referred to systems_of_equations_ex2, which uses
TransientLinearImplicitSystem and runs well. I changed to
TransientNonlinearImplicitSystem and rewrite the residual function based on
that.
Anyway, I list the results below as reference. Some screenshots attached as
well. Further suggestion's welcome.
case 1(good one): DirichletBoundary class used, no spurious velocity near the
wall
penalty 1.e8, residual 1.e-16~1.e-17, nonlinear convergence 7.28e-4
u in [-0.196,1.0]; p in [-110, +111]
DirichletBoundary_class.png
case 2(problem now): self coded penalty integral (see laminar2dnl.cpp), nonzero
velocity on the corner wall
penalty 1.e8, residual 1.e-9~1.e-10, nonlinear convergence 7.286e-4
u in [-0.203,1.07]; p in [-195, +197]
h_elem: 1.25e-2
h_elem_0.0125.png
h_elem_0.0125_corner.png
case 3(problem as well): self coded penalty integral (see laminar2dnl.cpp),
nonzero velocity on the corner wall
penalty 1.e8, residual 1.e-11~1.e-12, nonlinear convergence 7.28e-4
u in [-0.203,1.07]; p in [-195, +197]
h_elem: 1.0
h_elem_1.0.png
h_elem_1.0_corner.png
Cheers,
Zhenyu
-----????????-----
??????: "Vikram Garg" <[email protected]>
????????: 2015-03-18 01:45:12 (??????)
??????: Zhang <[email protected]>
????: "[email protected]"
<[email protected]>
????: Re: [Libmesh-users] Proper way of imposing Weak Dirichlet boundary
condition
Zhenyu, can you tell us what happens if you remove the h_elem term in your
penalty formulation ? Usually, we just set the penalty to a very large number,
and do not involve the mesh size in setting it. See example 3:
http://libmesh.github.io/examples/introduction_ex3.html
On Tue, Mar 17, 2015 at 8:09 AM, Zhang <[email protected]> wrote:
Dear Libmesher,
I tried to write an incompressible Naiver-Stokes solver based Libmesh.
Following features includes:
coupled pressure-velocity method
TransientNonlinearImplicitSystem used with
compute_jacobian(..) and compute_residual(..) run separatedly
Lid-driven cavity case for initial tests
BDF1 time marching
QUAD4 element,
vel_order=2, pres-order=1, both LAGRANGE elements
Pressure pinned at node_id=0
I tried DirichletBoundary class to impose the velocity BC, the code runs OK.
Now the problem is :
I coded myself the common penalty method for term
\int_{\Gamma_D}dt*\gamma/h*u*v,
and applied the forms in boundary integral part of jacobian function
Jxw_face[qp_face]*dt*penalty/h_elem*phi_face_[j][qp_face]
*phi_face_[i][qp_face]
and
Jxw_face[qp_face]*dt*penalty/h_elem*phi_face_[i][qp_face] *(u-u_bc)
at counterparts of residual function
the results show the boundary velocity not fully applied ,esp. at the side
walls near
the two top corners. Actually there are nonzero u normal to the local side
wall.
So I wonder anybody here will kindly show me some hints.
Furthermore, I tried applied the weak Dirichlet conditions by add futher
boundary integrals like
dt\int_{\partial\Omega} (-\mu\nabla \vec{ u}+pII)\cdot \vec{n}\cdot\vec{v} +
dt\int_{\partial\Omega} (-\mu\nabla \vec{ v}+qII)\cdot \vec{n}\cdot\vec{u}
at left and
dt\int_{\partial\Omega} (-\mu\nabla \vec{ v}+qII)\cdot \vec{n}\cdot\vec{u_bc}
The case is even worse.
I also attached the code, and I am looking forward to any suggestions. Many
thanks.
Zhenyu
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Vikram GargPostdoctoral Associate
Predictive Engineering and Computational Science (PECOS)
The University of Texas at Austin
http://web.mit.edu/vikramvg/www/
http://vikramvgarg.wordpress.com/
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things parallel software development, from weekly thought leadership blogs to
news, videos, case studies, tutorials and more. Take a look and join the
conversation now. http://goparallel.sourceforge.net/
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--
Vikram Garg Postdoctoral Associate
Predictive Engineering and Computational Science (PECOS)
The University of Texas at Austin
http://web.mit.edu/vikramvg/www/
http://vikramvgarg.wordpress.com/
http://www.runforindia.org/runners/vikramg
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by Intel and developed in partnership with Slashdot Media, is your hub for all
things parallel software development, from weekly thought leadership blogs to
news, videos, case studies, tutorials and more. Take a look and join the
conversation now. http://goparallel.sourceforge.net/
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