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

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

For a high Reynolds number simulation I can check the numerical accuracy of the velocity field by checking the Courant numer in the logfile (I use a fixed time step) - how can I check the numerical accurary when simulating low-diffusivity scalars?


Johan

________________________________
From: Nek5000-users <nek5000-users-bounces at lists.mcs.anl.gov> on behalf of nek5000-users at lists.mcs.anl.gov <nek5000-users at lists.mcs.anl.gov>
Sent: Friday, June 29, 2018 7:06:22 PM
To: nek5000-users at lists.mcs.anl.gov
Subject: Re: [Nek5000-users] Measure resolution for simulations with low-diffusivity scalars

What are you looking for? How can I get a bounded scalar solution for a given (low) diffusivity and resolution?

Stefan

-----Original message-----
> From:nek5000-users at lists.mcs.anl.gov <nek5000-users at lists.mcs.anl.gov>
> Sent: Friday 29th June 2018 17:44
> To: nek5000-users at lists.mcs.anl.gov
> Subject: [Nek5000-users] Measure resolution for simulations with low-diffusivity scalars
>
> 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
>
>
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