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Manufactured solutions for incompressible Navier-Stokes |
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March 24, 2013, 09:56 |
Manufactured solutions for incompressible Navier-Stokes
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#1 |
New Member
Italo
Join Date: Sep 2009
Posts: 4
Rep Power: 16 |
I am testing a solver for the incompressible Navier-Stokes equations using manufactured solutions. The code uses a 1st order projection method on staggered grid, very similar to the MAC method. I use 1st order time stepping and second order spatial derivatives.
If I choose a manufactured solution that is divergence-free, all works fine. I get second order convergence for a stationary problem. But if the manufactured solution is not divergence-free, the method drops to 1st order, even though I added the source term for the Poisson equation. I found some publications that also use divergence-free manufactured solutions, but none explain why. Must the manufactured solution be divergence-free? Isn't it possible to test the code with a more generic solution? It seems intuitive that it should work. When solving the Poisson equation on a square surrounded by Neumann boundary conditions, I must prescribe the pressure at one point. And that is exactly on that point that the error is big. And the error only shows up when using non-divergence-free manufactured solutions. |
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March 25, 2013, 09:14 |
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#2 | |
New Member
Mlohry
Join Date: Mar 2013
Posts: 2
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Quote:
Similarly, your numerical method would have to drop to first order if your solution contains discontinuities, so I wouldn't be surprised to see only first order convergence for any such solution. |
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March 25, 2013, 09:20 |
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#3 |
New Member
Italo
Join Date: Sep 2009
Posts: 4
Rep Power: 16 |
The manufactured solution is not a solution for the original NS equations. A source term must be added to the equations so that it becomes a solution.
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