Standing Wave: different solutions for different Courant and/or different Mesh

nuovodna · May 6, 2010, 10:40

I'm trying to solve a standingWave but i have multiple different results with changing mesh params and Courant number.
Test cases:
BC : four walls
Dimension: 1x1x0.1 (2d)
1/nu = 1060
Mesh divisions along orthogonal flow direction : 100
200
400
Courant number: 0.5 / 0.1 / 0.05 / 0.01

Kinetic energy plots are different. On Courant numbers the 0.1 and 0.05 offer comparable solutions. Numerical schemes (ddtScheme, divScheme, gradScheme) are essentially non influential. Any idea/suggestion ??

kumar · May 7, 2010, 03:51

what solver are you using. I had a similar expereince while using interFoam. The solution is very much mesh dependent and also very much dependent on CFL number.

bye
Suresh kumar

nuovodna · May 7, 2010, 05:18

Yes, i m using interFoam 1.6.x . In my opinion, the difference of solutions seems to be related with viscous term. Have you any idea??

kumar · May 7, 2010, 05:27

actually i am also studying a problem which involves waves but it is not a standing wave. I am studying liquid sheets. I was wondering if the problem is due to the surface tension term.

Also since my simulation is unsteady, i use second order schemes for time. In my experience the solution also varies a lot if you use different schemes. Just try doing that.

nuovodna · May 7, 2010, 06:58

hi kumar thanks for your reply.

1-I tried three ddtScheme (Euler, backward and CrankNicholson) but they offer the same solution. I understand that backward and Crank Nicholson are the only 2nd order temporal schemes available.

2-Surface tension is not responsible in this case because i set it to 0.

3- I try as written in http://www.cfd-online.com/Forums/ope...viscosity.html
a very simple viscous flow and results were not good.
I'm thinking about the term

- fvm::laplacian(muEff, U)
- (fvc::grad(U) & fvc::grad(muEff))
// - fvc::div(muEff*(fvc::interpolate(dev(fvc::grad(U)) ) & mesh.Sf()))

in Ueqn.H.

I try the second formulation (commented in the file) and results changes a lot.
Maybe someone has find an alternate formulation (perhaps 2nd order) or find numerical schemes better to solve viscous problems without turbulence model.

kumar · May 7, 2010, 07:40

Hello
Just one comment
how can the results of the Euler and Cranknicholson be the same if Euler is first order and Cranknicholson is second order.
In my case when i compare the results of the Euler case with the Cranknicholson case i see that the waves at the interface are damped in the first order scheme results and as a result of which the breakup of the sheet is much delayed.

regards
Suresh kumar

May 6, 2010, 10:40	Standing Wave: different solutions for different Courant and/or different Mesh	#1
nuovodna Senior Member Emanuele Join Date: Mar 2009 Posts: 110 Rep Power: 17	I'm trying to solve a standingWave but i have multiple different results with changing mesh params and Courant number. Test cases: BC : four walls Dimension: 1x1x0.1 (2d) 1/nu = 1060 Mesh divisions along orthogonal flow direction : 100 200 400 Courant number: 0.5 / 0.1 / 0.05 / 0.01 Kinetic energy plots are different. On Courant numbers the 0.1 and 0.05 offer comparable solutions. Numerical schemes (ddtScheme, divScheme, gradScheme) are essentially non influential. Any idea/suggestion ??

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May 7, 2010, 03:51		#2
kumar Senior Member Suresh kumar Kannan Join Date: Mar 2009 Location: Luxembourg, Luxembourg, Luxembourg Posts: 129 Rep Power: 17	what solver are you using. I had a similar expereince while using interFoam. The solution is very much mesh dependent and also very much dependent on CFL number. bye Suresh kumar

May 7, 2010, 05:18		#3
nuovodna Senior Member Emanuele Join Date: Mar 2009 Posts: 110 Rep Power: 17	Yes, i m using interFoam 1.6.x . In my opinion, the difference of solutions seems to be related with viscous term. Have you any idea??

May 7, 2010, 05:27		#4
kumar Senior Member Suresh kumar Kannan Join Date: Mar 2009 Location: Luxembourg, Luxembourg, Luxembourg Posts: 129 Rep Power: 17	actually i am also studying a problem which involves waves but it is not a standing wave. I am studying liquid sheets. I was wondering if the problem is due to the surface tension term. Also since my simulation is unsteady, i use second order schemes for time. In my experience the solution also varies a lot if you use different schemes. Just try doing that.

May 7, 2010, 06:58		#5
nuovodna Senior Member Emanuele Join Date: Mar 2009 Posts: 110 Rep Power: 17	hi kumar thanks for your reply. 1-I tried three ddtScheme (Euler, backward and CrankNicholson) but they offer the same solution. I understand that backward and Crank Nicholson are the only 2nd order temporal schemes available. 2-Surface tension is not responsible in this case because i set it to 0. 3- I try as written in http://www.cfd-online.com/Forums/ope...viscosity.html a very simple viscous flow and results were not good. I'm thinking about the term - fvm::laplacian(muEff, U) - (fvc::grad(U) & fvc::grad(muEff)) // - fvc::div(muEff*(fvc::interpolate(dev(fvc::grad(U)) ) & mesh.Sf())) in Ueqn.H. I try the second formulation (commented in the file) and results changes a lot. Maybe someone has find an alternate formulation (perhaps 2nd order) or find numerical schemes better to solve viscous problems without turbulence model.

May 7, 2010, 07:40		#6
kumar Senior Member Suresh kumar Kannan Join Date: Mar 2009 Location: Luxembourg, Luxembourg, Luxembourg Posts: 129 Rep Power: 17	Hello Just one comment how can the results of the Euler and Cranknicholson be the same if Euler is first order and Cranknicholson is second order. In my case when i compare the results of the Euler case with the Cranknicholson case i see that the waves at the interface are damped in the first order scheme results and as a result of which the breakup of the sheet is much delayed. regards Suresh kumar