[wizard8426]

Hi everyone, I am a PhD student in Taiwan. My background is electronic engineering, which means I am totally new to CFD.

Because my research demands, I need to write a CFD simulator.
Now I am following the book written by Versteeg "An Introduction to Computational Fluid Dynamics" to implement my own simulator.

I only need to simulate laminar flow for electro-osmosis behavior, so a simplified NS equation is good enough for me.

η∇^2(μ) = -∇p -qψ

η : viscosity
μ : velocity
p : pressure
qψ : coulomb force

It is a incompressible steady navier stokes equation, and only diffusion problem need to be considered. So I think FVM central difference is enough for this problem.

Now I am facing the following problems :

1. When I am using SIMPLE algorithm with coarse mesh, the simulator will converge very easily. But when I starting to refine the mesh, the simulator seems going to start oscillating and diverge. I need to lower the value of under relaxation coefficient for P' (AlphaP) to make the simulator stable. And of course, it will slower the converge speed.

For example, simulation area 10nm x 10nm (my length unit is nm.)
inlet flow = 1nm/s at left bounardary. Coordinate (0,4)~(0,6)
outlet flow = 1nm/s at right bounardary. Coordinate (10,4)~(10,6)
noslip boundary is applied.

20x20 nodes, AlphaP=0.01 diverge, AlphaP=0.005 converge
40x40 nodes, AlphaP=0.005 diverge, AlphaP=0.002 converge
50x50 nodes, AlphaP=0.002 diverge, AlphaP=0.001 converge
(When it converge, the simulation result seems reasonable and all of them looks identical.)

Is normal? Is there any way to find out a appropriate AlphaP without try and error?
I need to simulate about 100um * 100um area with several nm meshing step. This will take me forever.....


2. By tracing the simulation process, I found it seems because the velocity is not satisfied continuity equation, so the pressure will try the correct the velocity field. But when I using fine mesh, pressure field will over correct the velocity field and start oscillating.
Is this normal that the influence of pressure will increase as nodes increase?


3. Same problem also happens in SIMPLER algorithm, but this time I have no way to stabilize the simulator, because there is no under relaxation coefficient in SIMPLER algorithm.
After calculate pseudo-v and solve P by using pseudo-v, I found that this pressure field P will generate irrational velocity field and makes it diverge.
For example, initial guess inlet flow and outlet flow is 1 nm/s. Afer the calculation, somehow the maximum velocity will higher than 1.
But If I simulate different cases, sometimes it will still converge. (even faster than SIMPLE)
I have already check my code many times, but still no clue about this.


4. Is there any recommended code/solver on the internet for incompressible steady navier stokes equation with finite volume method?