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The second example is a classical benchmark test for incompressible flow: the cavity flow problem.
The same boundary conditions are used to solve the Stokes and the Navier Stokes problems.
As in the previous example, several mixed elements can be used in the computation.
It is also possible to solve the transient Navier-Stokes problem.
In this case, solution is computed using the Chorin-Temam projection method.
It is a two-step method: the first step includes the viscous and convective terms
whereas in the second one, pressure and the incompressibility constraint for
velocity are considered.
Figures below show streamlines of the solution computed using a mesh of 15x15 Q2Q1 elements.
Notice the position of the main vortex as Reynold's number is increased.
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Stokes |
Navier-Stokes with Re = 100 |
Navier-Stokes with Re = 1000 |
As in the previous example, pressure can not be computed accurately if inf-sup condition is not satisfied
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