Jeff Hiller
COMSOL Employee

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Posted:
9 months ago
Mar 10, 2020, 12:00 PM EDT

Updated:
8 months ago
Mar 17, 2020, 3:13 PM EDT

Hi John,

No, no additional equation is needed. If you think about it, you have (in 3D), 3 scalar equations for momentum conservation (one for each direction) plus one equation for mass conservation, and 4 variables (3 velocities and 1 pressure). So there's just the right number of unknowns for the number of equations. One Finite Element textbook that covers how to formulate such finite elements is Bathe's Finite Element Procedures. In my copy (ISBN 0-13-301458-4), this is covered in Section 7.4. I am sure the same info can be found online as well.

Best,

Jeff

PS:
If you introduced an equation of state, you'd be introducing an extra equation and an extra unknown (T), so that'd be OK too, but is not needed if the temperature is known.

Bernoulli is just an integral form of Navier Stokes, so it wouldn't add anything.

-------------------

Jeff Hiller

Hi John,
No, no additional equation is needed. If you think about it, you have (in 3D), 3 scalar equations for momentum conservation (one for each direction) plus one equation for mass conservation, and 4 variables (3 velocities and 1 pressure). So there's just the right number of unknowns for the number of equations. One Finite Element textbook that covers how to formulate such finite elements is Bathe's Finite Element Procedures. In my copy (ISBN 0-13-301458-4), this is covered in Section 7.4. I am sure the same info can be found online as well.
Best,
Jeff
PS:
If you introduced an equation of state, you'd be introducing an extra equation and an extra unknown (T), so that'd be OK too, but is not needed if the temperature is known.
Bernoulli is just an integral form of Navier Stokes, so it wouldn't add anything.

Jeff Hiller
COMSOL Employee

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Posted:
9 months ago
Mar 10, 2020, 2:06 PM EDT

Updated:
8 months ago
Mar 17, 2020, 3:13 PM EDT

Hi John,

Pressure is not computed from velocity. Pressure is treated as a separate dependent variable, with its separate dof's, interpolation functions, etc. You can find more information on this physics interface in the COMSOL Multiphysics Reference Guide, around page 904 (for version 5.5).

Best,

Jeff

-------------------

Jeff Hiller

Hi John,
Pressure is not computed from velocity. Pressure is treated as a separate dependent variable, with its separate dof's, interpolation functions, etc. You can find more information on this physics interface in the COMSOL Multiphysics Reference Guide, around page 904 (for version 5.5).
Best,
Jeff

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Posted:
8 months ago
Mar 17, 2020, 9:39 AM EDT

Hi Jeff, thanks for the reply. I feel there is still some assumption that must be missing? Is there an assumed equation of state that is being implemented something that relates pressure to volume and temperature maybe? Or perhaps Bornoulli's principle is being applied. I just dont see anything explicitly stated in the manual. Thanks for the help.

Hi Jeff, thanks for the reply. I feel there is still some assumption that must be missing? Is there an assumed equation of state that is being implemented something that relates pressure to volume and temperature maybe? Or perhaps Bornoulli's principle is being applied. I just dont see anything explicitly stated in the manual. Thanks for the help.

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Posted:
8 months ago
Mar 17, 2020, 12:21 PM EDT

Jeff, thanks for the help and the explanation.

Jeff, thanks for the help and the explanation.
- JB