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

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

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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