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question about the inertial term expression in Navier-Stokes equation

Posted 6 mar 2017, 15:58 GMT-5 Fluid & Heat, Parameters, Variables, & Functions Version 5.0 2 Replies

John Zhang
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Hi all,

I have a question about the inertial term expression in COMSOL.

As we know, the inertial term in Navier-Stokes equation is rho*u*del(u), rho is density, u is velocity vector.

While in COMSOL, the inertial term is written as rho*(u*del)u.

These two expressions are different.

Is there something wrong with the expression in COMSOL?

I am very appreciated that if you can answer my question.

Many thanks,

John
2 Replies Last Post 7 mar 2017, 08:49 GMT-5
Henrik Sönnerlind COMSOL Employee

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Posted: 8 years ago 7 mar 2017, 01:40 GMT-5
Hi,

You can find both versions in the literature. The form is slightly more explicit with respect to where the contraction (in the tensor sense) appears.

If you consider the index form, this term is . Without the parenthesis it requires a little more thinking not to end up in .

By the way, if you look at Wikipedia, you will find the form with parenthesis. en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations

Regards,
Henrik
Hi, You can find both versions in the literature. The form [math] (\mathbf u \cdot \nabla) \mathbf u [/math] is slightly more explicit with respect to where the contraction (in the tensor sense) appears. If you consider the index form, this term is [math] \rho u_j u_{i,j}[/math]. Without the parenthesis it requires a little more thinking not to end up in [math] \rho u_j u_{j,i}[/math]. By the way, if you look at Wikipedia, you will find the form with parenthesis. https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations Regards, Henrik
John Zhang
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Posted: 8 years ago 7 mar 2017, 08:49 GMT-5
Hi Henric,

Thanks for your explanation.

The inertial term is (u*del)u, not u*del(u).

Many thanks,

John
Hi Henric, Thanks for your explanation. The inertial term is (u*del)u, not u*del(u). Many thanks, John

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