CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > General Forums > Main CFD Forum

Arbitrary Choosing of the Solution Domain - Navier Stokes and Manufactured Solutions

Register Blogs Members List Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old   January 11, 2015, 10:33
Default Arbitrary Choosing of the Solution Domain - Navier Stokes and Manufactured Solutions
  #1
New Member
 
Fabian Gabel
Join Date: Oct 2014
Location: Darmstadt
Posts: 13
Rep Power: 8
eltenedor is on a distinguished road
I want to verify a finite-volume solver (SIMPLE-Algorithm) for the incompressible Navier-Stokes equations by using a manufactured solution. I use Dirichlet boundary conditions for the velocity at all boundaries. The manufactured solution for the velocities I use, is constructed as the curl of a vector field and thereby fulfills the continuity equation at any point.

Depending on how I choose the domain on which to solve the equations I run into convergence problems: The residual of the pressure correction equation stagnates after an initial decrease.

I am approximating the mass fluxes through boundary faces using the midpoint rule and apparently this leads to a net loss/gain of mass considering the entire problem domain.

Is this the normal behavior? Are there any remedies other than choosing a manufactured solution that identically vanishes at the boundaries? Would it be an option to provide the exact mass flux instead of the approximate (not sure if this is allowed, since the Dirichlet boundary condition only fixes the velocity)?
eltenedor is offline   Reply With Quote

Old   January 11, 2015, 15:53
Default
  #2
Senior Member
 
sbaffini's Avatar
 
Paolo Lampitella
Join Date: Mar 2009
Location: Italy
Posts: 1,419
Blog Entries: 19
Rep Power: 31
sbaffini will become famous soon enoughsbaffini will become famous soon enough
Send a message via Skype™ to sbaffini
The principle underlying the manufactured solution approach to the verification is that, for a given solver, you should be able to normally set-up the problem according to the known solution (thus, the appropriate set of Dirichlet/Neumann b.c. and source terms, when encessary).

If your solver does not produce the expected results than there is something wrong in it. Is this an in-house code or some commercial package?
sbaffini is offline   Reply With Quote

Old   January 11, 2015, 16:54
Default
  #3
New Member
 
Fabian Gabel
Join Date: Oct 2014
Location: Darmstadt
Posts: 13
Rep Power: 8
eltenedor is on a distinguished road
The Solver I use is neither commercial nor in-house - it is a modification of caffa I implemented for my masters thesis.

Apparently the global mass balance is not fulfilled when the boundary mass fluxes aren't calculated precise enough or the manufactured solution doesn't vanish on the boundaries. On the other side I was able to create solutions that are symmetric in the sense, that the mass fluxes on different sides of the problem domain complement each other, leading to a zero net mass flux over the domain boundaries.

I think a higher order of integration for mass fluxes at the boundaries might help. Note that I already verified the solver on problem domains that have the afore mentioned beneficent properties.

Unfortunately I don't have the ability and the time to confirm my suspicion by using another cfd tool. I was hoping someone of the community already had stumbled upon this exact problem and could share some insight.
eltenedor is offline   Reply With Quote

Old   January 11, 2015, 19:38
Default
  #4
Senior Member
 
sbaffini's Avatar
 
Paolo Lampitella
Join Date: Mar 2009
Location: Italy
Posts: 1,419
Blog Entries: 19
Rep Power: 31
sbaffini will become famous soon enoughsbaffini will become famous soon enough
Send a message via Skype™ to sbaffini
I am not very confident on the Peric codes but, is it possible that this is a staggered grid issue? I can't see why a 0 boundary value should be different from any other numerical value as long as the overall boundary integration still results in mass conservation.
sbaffini is offline   Reply With Quote

Old   January 12, 2015, 04:20
Default
  #5
New Member
 
Fabian Gabel
Join Date: Oct 2014
Location: Darmstadt
Posts: 13
Rep Power: 8
eltenedor is on a distinguished road
Quote:
I am not very confident on the Peric codes but, is it possible that this is a staggered grid issue?
I use a collocated grid arrangement.

Quote:
I can't see why a 0 boundary value should be different from any other numerical value as long as the overall boundary integration still results in mass conservation.
You are right. If you look again, this is not contradicting my previous post.

Quote:
On the other side I was able to create solutions that are symmetric in the sense, that the mass fluxes on different sides of the problem domain complement each other, leading to a zero net mass flux over the domain boundaries.
What I meant to say is, that even though locally at the boundary faces the boundary value of the velocity isn't zero, I accomplish a zero net mass flux (mass is conserved) due to the symmetry of my manufactured solution. If I am not able to use this symmetry, because the geometry of the used solution domain changes, the mass fluxes will not complement each other anymore, leading to a overall mass flux unequal to zero.

This effect can be weakened by using a finer grid (since my discretization is consistent) or by using a higher order of integration at the boundaries.
eltenedor is offline   Reply With Quote

Old   January 12, 2015, 08:35
Default
  #6
Senior Member
 
sbaffini's Avatar
 
Paolo Lampitella
Join Date: Mar 2009
Location: Italy
Posts: 1,419
Blog Entries: 19
Rep Power: 31
sbaffini will become famous soon enoughsbaffini will become famous soon enough
Send a message via Skype™ to sbaffini
I edited the post because i finally got your issue.

If i got it correctly, your manufactured solution is such that it is locally divergence free
but it preserves global continuity only for certain domain configurations.

Obviously what you are doing cannot be done and there certainly is a problem with either your manufactured solution
or the domain over which you are solving for it.

The domain you can use must be such that the manufactured solution preserves the global continuity.

This, at least, for incompressible solvers. It is a mathematical constraint for the well posedness of the pressure
equation.
sbaffini is offline   Reply With Quote

Reply

Tags
boundary conditions, mass conservation, navier-stokes, simple algorithm

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are On
Refbacks are On



All times are GMT -4. The time now is 05:09.