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Old   October 6, 2005, 12:58
Default deforming grid
  #1
sourabh
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I want to model a deforming grid problem with fixed no. of points, In finite volume framework withe explicit marching. Can I get any suggestion or referece something. Thank you for reading.
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Old   October 7, 2005, 02:53
Default Re: deforming grid
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ganesh
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Dear Sourabh,

Yes, it is definitely possible to model such a problem. However, it would be more intersting and clear if you could also specify the context of your problem, ie. what kind of problem you are in fact trying to solve. In general most unsteady flow problems that involve moving boundaries can be solved using a variety of methods, which include moving grid/deformin-grid formulations. If your work matches with the above to any extent you casn check the following papers for an initial reference.

And as far as deforming grids are concerned, with explicit marching the major changes to a non-deforming grid case are in the following.

1. The flux formula, the grid moves so the convection velocity is modified 2. The boundary conditions on the moving boundary, for which the grid is deforming 3. The FVM update formula and hence the marching, to incorporate the changing volumes.

J.T. Batina,AIAA Jl. Implicit flux split schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

Trepanier etal., AIAA Jl. Unsteady euler solutions for arbitarily moving bodies and boundaries

Venkatakrishanan and Mavriplis , AIAA paper 1995

These give some details for implicit marching also.

Hope this helps

Regards,

Ganesh
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Old   October 7, 2005, 08:30
Default Re: deforming grid
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Jessy
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For time-varying grids, you have to solve an additionnal conservation law for the cell volume. This is the so-called Geometrical Conservation Law (GCL) which is deduced from the general integral form of the Euler equations for a constant state (density = cst, velocity = cst, pressure =cst). You can find quite a lot of papers dealing with the GCL and the formulation of the numerical methods in this general framework.
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Old   October 8, 2005, 06:47
Default Re: deforming grid
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ganesh
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Dear Jessy,

Thaks for making the point, which I missed completely. However, it is to be noted that there has been a lot of controversy about the GCL and its use. While there has been only a little theoretical work on the GCL (Farhat etal 2002,2000), there have been several numerical experiments on the same. While some do not find any difference in the absence of the GCL, others have reported numerical instabilities and non-physical oscillations. However, in problems of aeroelasticity wherein there is an energy transfer/interplay between the fluid& structure, it is imperative that the GCL be used.(Farhat,1999). Although this is the case, I strongly support the fact that GCL is a must for any moving grid computation, to be on the safer side, both numerically and theoretically.

Regards,

Ganesh
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