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November 12, 2002, 19:35 
How to deal with "dummy" cells by FVM

#1 
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hi, there
I am using structured grid finite volume method to compute for a case. My problem is that there will be some cells that is occupied with solid. I think these cells definitely should not be included in the computation, so I called them "dummy" cells.(please correct me if the name is not right). However, since I am using an Euler solver, it seems there will be flux into these cells. For example, my domain is something like below(sorry for the bad drawing, maybe here should let us upload some pictures)  _______________ _______________ ____________***<solid cells ____________***<solid cells _______________                  Thanks for advice. 

November 12, 2002, 19:38 
Re: How to deal with "dummy" cells by FVM

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sorry for the drawing,I should preview them. it is something like: for example: 4x4 grid, with (2,3)(2,4)(3,3)(3,4) are solids.


November 13, 2002, 07:49 
Re: How to deal with "dummy" cells by FVM

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There are several techniques. One general method would be a technique very similar to that used multiphase flows by introducing a solid/fluid fraction say alpha. Alpha for the solid (solid fraction) indicates which part of the control volume is occupied by the solid: thus a value of one indicate completely occupied by a solid, a value of zero that the control volume is completely occupied by the fluid. Values in between indicates that percentage occupied by the solid. Thus the (fluid fraction) = 1 – (solid fraction) The conservation equations used is very much similar to the multiphase flow equations, all the terms contains the fluid fraction. When discretised with the finite volume method, the effect of Alpha*Volume indicates that part of the control volume that is available for the fluid. Thus a cell containing a solid will be zero * Volume. A subsequent issue is that the fluid fraction at the control volume faces should be defined as well. Thus, a solid covering 30% of a control volume face makes only 70% flow region available. According to your drawing (if I understand your "bad drawing" correctly) the faces values of your control volumes will either be one or zero. Once this solid fraction starts to move you have several additional problems that could be addressed quite efficiently.
Another very simple technique is to hard code the fluxes at solid control volume faces to be zero and for the purpose of the solver to make the matrix central coefficient of the control volumes containing the solids very large, say E+10. The inverse E10 is very small and the result of the solver is an unchanged value for the control volumes containing the solids. Hope this help 

November 13, 2002, 10:39 
Re: How to deal with "dummy" cells by FVM

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Don't believe that there's an universally accepted terminology for these cells. I've seen "solid". The Los Alamos folks used "obstacle" for years.
The ring of cells outside your active region that can be used to set boundary condition has  in my experience  been called "ghost", "imaginary", "dummy", "image" and probably some others I've forgotten. So "dummy" could lead to some confusion if it's published. The condition you need to impose is of course that there's no flow through the face of the obstacle cell. I think a previous post has given you a good solution for that. 

November 14, 2002, 03:40 
Re: How to deal with "dummy" cells by FVM

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My experience, as the two above, is that you should set the numerical flux at the wall surface to original physical flux. Ignore all the contributions from the ghost cells, else you will introduce artificial flux into the flow domain.


November 14, 2002, 16:05 
Re: How to deal with "dummy" cells by FVM

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to me, it seems to set zero flux by incorperate huge coefficient is a simple way. Thank you very much. But can you tell me how the boundary conditions on the solid surface are applied? Since I am solving Euler equation, a zero velocity at surface is not correct. thanks again.


November 14, 2002, 16:09 
thanks, Jim and versi

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November 15, 2002, 01:35 
Re: How to deal with "dummy" cells by FVM

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Apart from a possible pressure extrapolation problem where special care needs to be taken, should boundary conditions be catered for in a natural way. Unless you want to apply wall functions for turbulence modelling at these solid cell interfaces. Here some research needs to be done, especially if the cells are partially occupied by a solid.
Thus, if you need wall functions at these solid cell interfaces, you are in for some research and testing (maybe a PhD or two). Here, a faster remedy might be to adjust your coding in such a manner that you can solve for block structured meshes. Alternatively, you should use a very fine mesh near the solid cells. GOODLUCK 

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