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B.C. for N-S equns on Unstructured grid

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Old   January 18, 2001, 01:45
Default B.C. for N-S equns on Unstructured grid
  #1
Abhijit Tilak
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hi, all

I want to know where and how to specify B.c (wall, inflow, exit, symmetry on unstructured grids) for Viscous Navier Stokes. I am little confused as to where to specify B.C 's on edge or node or cell center. i am currently using cell based data structure (collocated and values stored at cell centers). can anybody give references or some tips.

thanks abhijit tilak
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Old   January 18, 2001, 04:23
Default Re: B.C. for N-S equns on Unstructured grid
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John C. Chien
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(1). I think, the proper step is to first define your computational domain and the boundary conditions, along with the governing equations. (2). Once you have done this, the governing equations and the boundary conditions will remain the same. (3). Next, the computational domain can be divided into cells, or covered with a mesh. You can then transform the governing equations into finite-difference or finite volume form. You also transform the boundary conditions in the same way. It doesn't matter whether the boundary condition is positioned right on the grid point (or the grid point is positioned on the boundary) or not, the condition remains the same. (4). For example, if you are using the Cartesian mesh and the boundary does not go through the grid points, then you will have to develop special schemes to implement the boundary condition through the given mesh points. You can find such examples in many numerical method text books, when solving heat conduction problems. (5). The same principle applies to what you are doing. You can place the cell center right through the boundary, or you can place the edge of the cell on the wall. It is completely up to you. But the boundary conditions remain the same. You can also cut the boundary through the existing cells. It is up to you to develop the schemes to implement the original boundary condition on your mesh. What I am trying to say is that, the mesh is just mesh, and it does not have to be lined up with the boundary conditions. Although I think, it would be easier to make use the cell or mesh properties such that the original boundary conditions can be implemented easily. But that is purely up to you.
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Old   January 23, 2001, 07:51
Default Re: B.C. for N-S equns on Unstructured grid
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Kang, Seok Koo
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I think your comment is a little .. abstract and superficial. He and other readers, including me, want detailed information, i think. Can you please describe some examples of implementing boundary conditions. I suppose, many readers are confused when the cell-centered scheme is used. Put the boundary on the cell center or the edge? And what is the accuarcy of the approximation at the boundary? (1st or 2nd order etc.). How to use characteristic equation at the boundary when the grids are unstructured.

Regards,

Kang, Seok Koo.
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Old   January 23, 2001, 13:02
Default Re: B.C. for N-S equns on Unstructured grid
  #4
John C. Chien
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(1). Please read the book by Joe H. Ferziger, Milovan Peric, " Computational Methods for Fluid Dynamics". (2). It covers the finite-volume methods, treatment of boundary conditions, and examples in great detail. (3). You have to realize that there are a lot of approximation involved in deriving the equation and boundary conditions, especial for finite-volume methods. (4). So, there is no standard method to follow. And I am sure that both mesh distribution and the approximation will also have impact on the convergence of the solution. (5). The same is true for the finite difference method. Even though it is much more straight forward in finite difference method, still there are many ways to handle the boundary conditions, say at the wall. You can use extra point outside the domain, simple one side difference, or higher order one side difference, or interpolations. (6). I think, your question is a very good one. But numerical approximations in CFD are more or less individual's invention, up to this point. That's why most technical papers and commercial codes simply do not describe the actual method used in detail. That is the reason why in commercial codes, there are many options available. If there is a good one, then all they need is one standard method without options. (7). If you can get the converged solution by assuming a constant and uniform value at the boundary, then just do it. If it does not work, then change it to linear interpolation or something else. (8). So, you are free to experiment with methods used in the book, or technical papers, or even your own invention. If there is a standard method, then everyone would be using the same code, getting the same answer, with no convergence problem at all. (9). In CFD, there is a huge gap between the books, the codes, and the converged solutions. By the way, because of the health condition of .com business, the free Internet connection is being limited. So, I will have to look for another sources. As you see, in real world nothing is free. If you don't invested in books and the time to read it, then it is your business. My free service is also limited by the free Internet services.
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Old   January 24, 2001, 00:08
Default Re: B.C. for N-S equns on Unstructured grid
  #5
Abhijit Tilak
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hi friends,

i think we are deviating from main topic. i don't expect someone who answers my queries to key in the full answer. i have asked for tips and references. if u can provide that, i am more than happy. i had also gone through earlier postings on the B.C for unst. grids.

thanks abhijit
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