BDF order setting on the example "Vortex shedding"

Numerical methods and mathematical models of Elmer
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thomasatelmer
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BDF order setting on the example "Vortex shedding"

Post by thomasatelmer »

Hello, Elmer users and creators,

I have so far used Elmer in various physical disciplines sufficiently successful (time-dependent thermomechanics, coupled FSI, magnetics ...). Now I am on to assessing the thermal air flow by convection. For this, I firstly ran the GUI example for the vortex shedding phenomenon from the GUI tutorials. All works fine and quickly, so the example lends itself to playing around to find sensitivities. I realized, that the BDF order was set to 2, whereas for any other transient calculations for heat etc., I used 1 in the past (Nowadays, I assume this was correct, for reason given later). In my trials, I found for sure a dependence on the viscosity and density of the ideal fluid used, and as well and dramatically to the BDF order. I understand that the BDF order is the polynominal order of a function, that makes a new timestep inherit field conditions from the past timestep(s). On the vortex example, it decides upon if the solution shows a small vorticity (1, 2) or a highly turbulent field (4, 5). This is ok and does not surprise me, but I wonder now, how to figure out, what the correct BDF order would be to resemble something close to reality? Do I have to make a test and validate the setting by similarity of simulation with reality in each case, or would someone have a simpler or more effective idea? This all said with being a hands-on engineer with some physics background, but less mathematical background... :oops: )

I am looking forward to your thoughts,
Thanks, Thomas.

p.s. I think the BDF order of 1 for a transient heat simulation is just fine, as thermal processes are slow and highly damped by thermal capacities (much like a highly viscous fluid in the Vortex case).
kevinarden
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Re: BDF order setting on the example "Vortex shedding"

Post by kevinarden »

I believe the BDF order increase the staibility of the solution, i.e if the solutions converges or diverges. The increased order comes with a computational cost. I do not think the order effects the accuracy of the solution unless you modify the convergance criteria for a given solution. So there isn't really a "correct" BDF order, nunerical solutions of differintial equations are approximations, so most solutions try to get the best or adequate approximation for the least computational effort. An approach on a new problem would be to start with a BDF1 if it diverges using the desired criteria then a higher BDF might allow for convergence.
raback
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Re: BDF order setting on the example "Vortex shedding"

Post by raback »

Hi Thomas

The reason why the vortex shedding case is sensitive to BDF order is because it is sensitive to everything else too. The space and time resolution for the example are probably quite far from getting exact results. This is meant to be more like an educational example. The onset to instability is quite an instable thingy ;-) Most things are not as instable. Generally higher order BDF may be advantageous. There may be exceptions to this like some multiphysics problems, phase change, contact mechanics etc.

-Peter
thomasatelmer
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Re: BDF order setting on the example "Vortex shedding"

Post by thomasatelmer »

Thank you, Kevin & Peter, for the as-always swift replies.

I understand your statements such, that BDF orders should generally not change the overall characteristics of the solution result, but can increase stability when higher orders are used. If a physically instable problem like the vortex shedding is looked at, the reliability of the solution is generally low. But what about cases, where natural convection for cooling is looked at - would that also be regarded as physics that can only be simulated with low reliability? (This is the background of my endeavour...) It also involves possible vortices in the flow...

Thanks and Regards,
Thomas.
kishpishar
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Re: BDF order setting on the example "Vortex shedding"

Post by kishpishar »

Hi Thomas,

Generally higher order BDF may give you an edge with respect to numerical stability of the solution, but that might not be the bottleneck in simulating natural convection. Simulating natural convection to a high degree of fidelity is notoriously difficult, mostly due to the highly unstable nature of the physical phenomena. Such flows seldom reach any steady state, so the best bet is to compute the transient behavior with very small time steps. I don't think the order matters much as there are other factors which exert larger influences on the solution like mesh quality, size and resolution and temporal resolution etc. Further, the nature of the flow itself, like laminar, turbulent or transitional - usually assessed by global calcultions of Rayleigh and Grashof numbers and comparisons with some empirical correlations. If turbulent, you will need to add a turbulent solver along with Navier-Stokes and Heat solvers.

-Kumar
thomasatelmer
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Re: BDF order setting on the example "Vortex shedding"

Post by thomasatelmer »

Hello, Elmer forumists, and thank you for your thoughts on my questions so far.

I went a little further with my trials and modeled a 3D case of a steel cylinder of T=373K in surrounding resting air of 293K. I was able to get convection (ok, no turbulence, but it looks quite similar to reality, with hot air rising to the top of a room and distributing there, dropping at the cool walls etc.). However, I also wanted to see how quickly the steel cylinder would cool, to assess heat transfer coefficients of the slowly rising air. Therefore, I gave the cylinder a start temperature of 373K but did not pose additional heating during the simulation run or set a temperature on the body or the cylinder surface. But - and this is my problem, I saw that the cylinder started with 373K at its inside, but the outside skin was 293K. For some reason, the initial condition of 373K does not apply at the surface elements of the body. Could someone comment on this behaviour, whether it is intended (or a flaw in my setup) and how to get the complete cylinder to be at a homogenous temperature at the initial start, please? I attach screenshots and SIF file for your review.

Thank you - enjoy the evening,

Thomas.
Attachments
case.sif
Body 1 is the cylinder
(3.85 KiB) Downloaded 202 times
at timestep 1
at timestep 1
temp_cylinder.png (31.78 KiB) Viewed 3693 times
result_cut.PNG
result_cut.PNG (58.81 KiB) Viewed 3693 times
kevinarden
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Re: BDF order setting on the example "Vortex shedding"

Post by kevinarden »

I beleive that the temperature is calculated at the nodes, but the node on the outer sking of the cylinder is also the node attached to the air element. Therefore if the air is cooler than the cylinder than I believe the nodal temperature is the average of all of the elements attached to it. I have found for this type of problem the boundary results are sensitive to mesh density.

This post may give your another example. Notice a T=0 the boundary looks like an average of the two bodies.

viewtopic.php?f=18&t=3969
thomasatelmer
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Re: BDF order setting on the example "Vortex shedding"

Post by thomasatelmer »

Good evening, Kevin,

thank you for your assessment and what you tell me sounds quite logical to me. So I thought about what to do... I didn't want to mesh my volume so fine as to minimize the effect, so I decided to model a 1mm thick layer of air around the cylinder and set this layer also to 373K at the start. As it is air, it gets equalized quickly during the first time steps, and now the correct cooling pattern is seen on the cylinder surface (cooler at the bottom, hotter at the top over time), and the whole cylinder volume starts at 373K flat. It is a workaround, but I would guess it does affect the match of simulation to reality less than if the cylinder would have different temperature across its volume. The funny part comes when the body in air is no plain cylinder any more - modeling an equidistant shell probably is quite tedious for a more complex geometry.

Thank you for your help, it made me be successful in the end :-)

Greetings, Thomas.
raback
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Re: BDF order setting on the example "Vortex shedding"

Post by raback »

Hi

There is a newer version of HeatSolve, HeatSolveVec, that comes partly with different features. One such feature is that you can create a discontinuity between bodies and give the interface a heat transfer coefficient. The cool thing with this is that it does not affect the mesh. It uses Discontinuous Galerkin machinery which is eliminated except that the interface, sort of reduced basis. You can find some examples with "DG Reduced Basis" among the tests. At the same time you can have PDEs that are not discontinuous.

-Peter
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