# interFoam fvSchemes for Convection Equation

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February 7, 2012, 23:29
interFoam fvSchemes for Convection Equation
#1
Member

Jim Carow
Join Date: Apr 2010
Location: Michigan, USA
Posts: 41
Rep Power: 8
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 Cauchy-Green deformation tensor (B) which is calculated by an equation (similar to an upper convective derivative):

Code:
```   gradU = fvc::grad(U);

fvSymmTensorMatrix BEqn
(
fvm::ddt(B)
+ fvm::div(phi, B)
==
twoSymm(B & L)
);```
As a test case I am solving a lid drive cavity case with a viscoelastic solid disk as the second phase. The fluid velocities and behavior seems correct however I am observing 'ripples' on the surface of the disk which seem artificial (please see the attached). The solid also orbits around the cavity faster than the benchmark.

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;
}```
and

Code:
```PISO
{
momentumPredictor yes;
nCorrectors     3;
nNonOrthogonalCorrectors 0;
nAlphaCorr      1;
nAlphaSubCycles 2;
cAlpha          2;
}```
thank you,

James
Attached Images
 wiggles.png (13.2 KB, 94 views) wiggles2.png (17.4 KB, 86 views)

 February 8, 2012, 04:06 #2 Senior Member     Anton Kidess Join Date: May 2009 Location: Delft, Netherlands Posts: 1,151 Rep Power: 20 I don't know about your specific case, but if you want to limit numerical diffusion MUSCL and SuperBee schemes work quite well. __________________ *On twitter @akidTwit *Spend as much time formulating your questions as you expect people to spend on their answer. *Join the OpenFOAM stackexchange Q&A site: http://area51.stackexchange.com/prop...oHPxcPqde7HtA2

 April 19, 2012, 23:17 'Wiggles' and 'Wrinkles' #3 Member     Jim Carow Join Date: Apr 2010 Location: Michigan, USA Posts: 41 Rep Power: 8 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 non-zero 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 immiscible-fluid and free-surface flows. Chemical Engineering Journal, 141(1-3), 204-221. 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 Senior Member     Anton Kidess Join Date: May 2009 Location: Delft, Netherlands Posts: 1,151 Rep Power: 20 Section 4.2 of this paper mentioned grid-alignment 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. __________________ *On twitter @akidTwit *Spend as much time formulating your questions as you expect people to spend on their answer. *Join the OpenFOAM stackexchange Q&A site: http://area51.stackexchange.com/prop...oHPxcPqde7HtA2

 July 15, 2013, 15:51 Left- #5 New Member   bryan Join Date: Nov 2012 Posts: 6 Rep Power: 5 I've also been trying to use the left-cauchy 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 Member     Jim Carow Join Date: Apr 2010 Location: Michigan, USA Posts: 41 Rep Power: 8 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 New Member   bryan Join Date: Nov 2012 Posts: 6 Rep Power: 5 I'm actually working on a viscoelastic fluid model for blood where the left-cauchy 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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