[Nek5000-users] Measure resolution for simulations with low-diffusivity scalars

[nek5000-users at lists.mcs.anl.gov]

Hi,


I want to evolve a scalar field \phi in my simulation with as low diffusivity (conductivity/(rhocp)) as possible.

I have performed simulations with sequentially reduced diffusivity D:


Simulation 1: D = 1*2.17*10^-5 m^2/s, polynomial order 7

Simulation 2: D = (1/4)*10^-5 m^2/s, polynomial order 7

Simulation 3: D = (1/4)*2.17*10^-5 m^2/s, polynomial order 11

Simulation 4: D = (1/8)*2.17*10^-5 m^2/s, polynomial order 11


Reducing the diffusivity, I keep the ratio D/dt constant, where dt is the time step.

At t = 0 \phi is bounded to 0 <= \phi <= 1, and it has no sources or sinks.

Currently, I check the resolution of the simulation after 25 s, by observing the range of \phi.

I find these values:


Simulation 1: -0.01 < \phi < 0.06

Simulation 2: -0.23 < \phi < 0.61

Simulation 3: -0.044 < \phi < 0.16

Simulation 4: -0.4 < \phi < 0.91


Indeed, the smaller the diffusivity D becomes, the worse resolution of \phi becomes.

Also, it seems as increasing the polynomial order improves the resolution of \phi.

However, the Courant numbers in my simulations are (on average):


Simulation 1: C = 0.31

Simulation 2: C = 0.06

Simulation 3: C = 0.14

Simulation 4: C = 0.06


That the Courant number goes down with increasing diffusivity is (I think) just  a consequence of reducing the time step (keeping the ratio D/dt constant).

According to the Courant number, I have really great resolution in Simulation 4, but according to the range of \phi I have not. Also, the Helmholtz solver seem to reach the tolerance in fewer iterations for low values of D.


Can somehow Nek output a measure of the resolution of a scalar field?

How can I improve the resolution at a low D/allow for lower D and keep a good resolution?


Best,


Johan


-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/nek5000-users/attachments/20180629/d0154536/attachment.html>