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Why can the weak forms of the Stokes and continuity equations be combined into a single equation?

To get from weak form I to II, just add the two equations of weak form I. To see the other direction, note that weak form II has to hold for all test functions $\phi$ and $\psi$. That is, you can test ...
• 451
Accepted

Non-standard boundary condition for incompressible Navier Stokes

I managed to resolve the issue, Need to compute the values only for the inner part of the domain, then apply BC for the boundary values. The only issue is that there is a backward scheme at the ...
• 362
Accepted

How to calculate the force of solid applied by fluid? Using finite difference method, DNS, staggered grid, SIMPLE algorithm, immersive boundary

The question is solved. I use wrong coefficient formula. I should use 2d formula but actually I use 3d. And my calculation method using momentum conversation may be wrong, but that is fine, I can use ...
Accepted

How to address the element face adjacent to boundaries when the finite difference method and marker-and-cell scheme are used to solve the Stokes flow?

The paper is not specifying a Dirichlet $v=0$ at $y=1$, but $u=u_D$ at $y=1$. This could be used as a wall slip condition: for $u_D=0$, you have a no slip boundary wall; that is, the flow tangential ...
• 2,794
1 vote

How to approximate the flux when using finite volumes?

The integral may be approximated with  \begin{align} \int_{\partial \Omega} \boldsymbol{\mathcal{F}} \cdot \vec{n} ~ds \approx \sum_k L_k \mathbf{T}^{-1}\vec{F}\left(\mathbf{T}~ \vec{u}\right) \end{...
• 1,335

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