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April 2, 2007, 06:13 
Hello Hrvoje,
I tried the ver

#21 
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Rolando Maier
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Hello Hrvoje,
I tried the version you sent me and experimented with it. For my testcase I noticed two things. The testcase is a mesh moving, with a constant velocity and a relative flow in the moving direction. I use the icoDyMFoam solver, where I activated the fvc::ddtPhiCorr() term in the PISO loop and I use the backward time scheme. 1) If I use a dynamic timestep the timestep adjustment is far more stable than without using this term. But it is still sensitive to the initial timestep (see above). 2) If I use a constant timestep the results are slightly worse than without the fvc::ddtPhiCorr() term. This refers to the solutions of U and p. Phi and meshPhi however is calculated correctly. This is caused by the method fvcDdtPhiCoeff(), which seems to be a weighting factor in fvc::ddtPhiCorr(). The problem appears, as in this method the difference between the "real fluxes" and the fluxes built by the velocity is slightly different. To overcome this trouble, I introduced an additional artificial weighting factor, which accounts for the change of phi in the past. backwardDdtScheme<type>::fvcDdtPhiCorr then reads: if (mesh().moving()) { . . return tmp<fluxfieldtype> ( new fluxFieldType ( ddtIOobject, rDeltaT *fvcDdtPhiCoeff(U.oldTime(), phi.oldTime()) *min(mag(phi.oldTime()  phi.oldTime().oldTime()) / mag(phi.oldTime()), 1.0) *( ( fvc::interpolate(rA*V0oV) *coefft0*phi.oldTime()  fvc::interpolate(rA*V00oV) *coefft00*phi.oldTime().oldTime() )  ( fvc::interpolate ( rA* ( coefft0*U.oldTime()*V0oV  coefft00*U.oldTime().oldTime()*V00oV ) ) & mesh().Sf() ) ) ) ); . . } For my case this seems to cure the problem and the results of p and U are what they should be. Rolando 

April 3, 2007, 07:53 
Hi everybody,
I also observ

#22 
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Frank Bos
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Hi everybody,
I also observed the problem with backward scheme in combination with a variable timestep. Using a custom dynamicFvMesh library I let the internal mesh points oscillate to create changing cell volumes. In such a way, using a uniform freestream, I could check if the solution is not influenced by the mesh motion and if the Geometric Conservation Law is satisfied. Summarising, I got no problems with CrankNicholson or Euler using constant and variable timesteps. Using backward I obtained a different from freestream solution when the timestep was varying. With constant timestep the solution was OK with the backward scheme. Together with a colleague (who knows more about time integration schemes than I do) we found a solution to this problem, which lies in backwardDdtScheme::meshPhi. I will briefly explain the principle of the solution. The ddt is properly defined as: phi(n+1) = ((3/2)V(n+1)  2V(n) + (1/2)V(n1)) / dt_1 This is solved using the values of the flux phi on timesteps n1/2 and n+1/2: phi(n1/2)=(V(n)V(n1))/dt_0 phi(n+1/2)=(V(n+1)V(n))/dt_1 Here dt_1 is the current and dt_0 the previous timestep. As far a we could see you need to make a correction in meshPhi for the fact that you have to use the dt_0 in the above line. Therefore we multiplied the coefft00 from backwardDdtScheme::meshPhi with dt_0/dt_1. When the timestep is constant, i.e. dt_0=dt_1, this ratio equals 1 and you will get the correct solution. So we changed: scalar coefft00 = deltaT*deltaT/(deltaT0*(deltaT + deltaT0)); Into: scalar coefft00 = deltaT/(deltaT + deltaT0); Now I obtain the correct solution using backward differencing on a moving mesh with variable timestep. Regards, Frank
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Frank Bos 

April 3, 2007, 08:06 
Did you make this change to co

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Did you make this change to coefft00 only in backwardDdtScheme<type>::meshPhi or also in all the ddt functions in backwardDdtScheme.C?
Henry 

April 3, 2007, 09:00 
I have redone the derivation o

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I have redone the derivation of the backward scheme for moving meshes and I agree with your change and will include it in the 1.4 release. Thanks a lot for the help in resolving this problem.
Henry 

April 3, 2007, 09:31 
Allright. From now on we can s

#25 
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Frank Bos
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Allright. From now on we can safely use this secondorder backward scheme.
If you still need the answer to your last question, here it is....I only changed the coefft00 in the backwardDdtScheme::meshPhi. In all ddt functions the definition of coefft00 is still OK, since at those places the current timestep dt_1 was used, according to the definition of ddt. Only there were you need the 'n+1/2' and 'n1/2' values, which is in meshPhi, this definition of coefft00 needs a correction. Frank
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Frank Bos 

April 3, 2007, 09:46 
Yes I agree.
Henry

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Yes I agree.
Henry 

April 3, 2007, 10:34 
Thanks a lot for that post Fra

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Rolando Maier
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Thanks a lot for that post Frank,
I tested it and the timestep oscillations are no longer present. Rolando 

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