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February 7, 2012, 23:29 
interFoam fvSchemes for Convection Equation

#1 
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Jim Carow
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Location: Michigan, USA
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I have been implementing a solver for one phase of fluid and a second phase of viscoelastic solid based on interFoam. The constitutive equation for the solid depends on the left CauchyGreen deformation tensor (B) which is calculated by an equation (similar to an upper convective derivative):
Code:
gradU = fvc::grad(U); L = gradU.T(); fvSymmTensorMatrix BEqn ( fvm::ddt(B) + fvm::div(phi, B) == twoSymm(B & L) ); I suspect numerical diffusion from the upwind differencing scheme used in the solution of BEqn. Sorry for the discourse but can anyone suggest alternative schemes or PISO settings which might improve this? I am using the following: Code:
divSchemes { default none; div(rho*phi,U) Gauss limitedLinearV 1; div(phi,alpha) Gauss vanLeer; div(phirb,alpha) Gauss interfaceCompression; div(phi,B) Gauss upwind; } Code:
PISO { momentumPredictor yes; nCorrectors 3; nNonOrthogonalCorrectors 0; nAlphaCorr 1; nAlphaSubCycles 2; cAlpha 2; } James 

February 8, 2012, 04:06 

#2 
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Anton Kidess
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I don't know about your specific case, but if you want to limit numerical diffusion MUSCL and SuperBee schemes work quite well.
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April 19, 2012, 23:17 
'Wiggles' and 'Wrinkles'

#3 
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Jim Carow
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Thanks for the input on the convection schemes. I can run with UMIST and SFCD applied to the convection term in the equation above but QUICK, MUSCL, and SuperBee lead to segmentation faults.
Since then I've learned the issue shown in the attached images wasn't numerical diffusion, although maintaining a sharp interface is always a good thing. I am still looking for an explanation for the presence of the artificial 'wiggles' or 'wrinkles' which appear on the interface using interFoam's interfaceCompression scheme and a nonzero value for cAlpha. If you have a look at a nice comparison of VOF methods in: Gopala, V. R., & van Wachem, B. G. M. (2008). Volume of fluid methods for immisciblefluid and freesurface flows. Chemical Engineering Journal, 141(13), 204221. doi:10.1016/j.cej.2007.12.035 You will see the same artificial wiggles present in the results of their simulations performed with interFoam, though there is no specific mention of this issue. In my cases there were no forces due to surface tension and I believe that such forces stabilize the interface an counteract the artificial distortion. Does Weller's scheme used in interFoam depend on the presence of surface tension? thanks and regards, Jim 

April 23, 2012, 08:42 

#4 
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Anton Kidess
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Section 4.2 of this paper mentioned gridalignment of the interface: http://powerlab.fsb.hr/ped/kturbo/op...InterTrack.pdf
It looks like the only thing you can do is reduce the time step.
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July 15, 2013, 15:51 
Left

#5 
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bryan
Join Date: Nov 2012
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I've also been trying to use the leftcauchy green tensor in a new solver with this code.
I was just wondering what you used for your boundary and initial conditions for B?? 

July 15, 2013, 16:08 
BC and IC's for B

#6 
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Jim Carow
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Hello,
I used the initial conditions B=I, identity since the body was initially undeformed, and I used zeroGradient conditions for the BC's. If you are advecting the tensor B you will likely face the challenge of diffusion based on the convection schemes I mentioned in this post. I ended up having best success with the using the CICSAM scheme (available in OF extend version ShipHydroSIG) for advecting the scalar field alpha. Curious to know what you are working on. regards, Jim 

July 15, 2013, 16:36 

#7 
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bryan
Join Date: Nov 2012
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I'm actually working on a viscoelastic fluid model for blood where the leftcauchy tensor is needed for the stress constitutive equation.
I'm still not entirely sure if this method for finding B will work in my case but I was planning to test it out as a first try. 

Tags 
diffusion, fvschemes, interfoam, viscoelasticfluid 
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