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Solving momentum Equation from known pressure field

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Old   July 8, 2021, 04:43
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Arjun
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Quote:
Originally Posted by sbaffini View Post
Even if the approach is based on:

1) A non pressure-free method (where GRAD(p_n) is used in first advancing u_n to u*)?

2) A mass flux that, for a given velocity field, is mass preserving only if based on the pressure correction for the current flow field u*?

My doubt, in these conditions, is on the practical reachability of the same steady state achieved with the correct algorithm and independently from the case.

Analytical solutions are nice, but typically hide certain exact balances between terms (e.g., in the Taylor solution the pressure gradient always balances the convective term) which might mask some issues.

Speaking only for Finite Volume Collocated solvers, the pressure only ends up in fluxes via dissipation like Rie and Chow dissipation for example. The way it does is that for smooth pressure the dissipation should theoritically be 0.


What it means is that pressure gradient is only source term (from pressure) in momentum equation. One should be able to get the velocity field for this source term ( -grad of P).

Now due to descretization errors the dissipation is not 0 but it is very small. If it is not small then one need to fix his code.
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Old   July 8, 2021, 04:44
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Originally Posted by FMDenaro View Post
No Paolo, I am talking about the discretized Hodge decomposition at the steady state. If you provide the discrete pressure gradient that satisfies

Div Grad p = Div a*

With the correct BCs you should be able to solve for V.
OOOOOOOHHHHH.... Now I see what you all mean, you're talking about solving one steady state equation once to full convergence.

Ok, I think I agree in general terms, yet I'm not convinced that this is independent from how you treat the non-linearity of the convective term
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Old   July 8, 2021, 05:25
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Quote:
Originally Posted by sbaffini View Post
OOOOOOOHHHHH.... Now I see what you all mean, you're talking about solving one steady state equation once to full convergence.

Ok, I think I agree in general terms, yet I'm not convinced that this is independent from how you treat the non-linearity of the convective term
Yes, I am talking of solving directly the steady state equation. The discretization of the non linear term must be coincident. The source term in the pressure equation and the discretization of the momentum equation.
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