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:[email protected] <[email protected]> Sent: Friday 29th June 2018 17:44 To: [email protected] 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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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 <[email protected]> on behalf of [email protected] <[email protected]> Sent: Friday, June 29, 2018 7:06:22 PM To: [email protected] 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:[email protected] <[email protected]> Sent: Friday 29th June 2018 17:44 To: [email protected] 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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