Hello there, I am trying to implement a time-dependent incompressible Navier-Stokes flow, and it ‘sorta works’, but it gets unstable at the outlet when the velocity gets high. I have tried to run the code on a finer mesh and with smaller time steps, but that does not change anything about the inst…

After further investigation it has proved, that the instability is a problem with small viscosities. With nu=0.1 there are no problems. @dokken do you know how to work around that?

As the Reynolds number directly relates to the viscosity, this is not suprising. As written in the fenics tutorial . First of all, it shows that all fluids behave in the same way: it does not matter whether we have oil, gas, or water flowing between two plates, and it does not matter how fast the fl…

Hi dokken, Does that mean that all the equations in Fenics (incl. tutorials) should be (are) given in dimensional values? And if so, what are these dimensions? Reading from the section you cited, I am confused on why we cannot formulate a weak formulation and a variational problem for the dimensi…

The dimensions in FEniCS is whatever you set them to. If you input a mesh of length 1, it is you as the user who decides if it is given in mm, m or km. They key is that one must make sure every input parameter has the same dimension. If you read through the rest of section 3.4.3, it states that it …

Thank you for that! I tried to solve the channel problem with H,L=1mm and aiming for a maximum velocity of 0.01m/s. That results (according to the book) to a Dp of 8e+4! That can be correct, right? The numerical solution blows up almost immediately…

So what is your visocity and density? The Reynolds number less than 100 should be fine.

I have tried both the following case: rho = 1, mu = 1 rho = 1000 (kg/m3), mu = 0.001 (Ns/m2) Aiming for velocity of 0.01m/s for a channel of height 10-3 (so 0 < y < H). According to the book, the value β for the inflow pressure is 8*umax/H^2 (just by changing the assumption U=H=1). But that give…

The second case will Give an extremely high reynolds number, and is definitely not feasible. In general, your parameters gives a very high dP as you have made the channel very short, and the pressure has to drop from 8 to 0 in 1e-3 meters.

The second case gives a Reynolds number of 10, why is that high? I want to find the “correct” Dp in order to get that desired max velocity. Could a potential longer channel fix the issue? Thank you :slight_smile:

Mixed incompressible Navier-Stokes

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dokken November 16, 2020, 1:53pm 2

I would suggest starting with verifying your solver using the Taylor-Green vortex problem or the DFG-2D benchmark, which are both covered in: Boundary Conditions & Convergence for 3D Navier-Stokes

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Mixed incompressible Navier-Stokes

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