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August 21, 2000, 11:25 
Mooving Grids

#1 
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Hi, I implemented mooving grids in my flow solver and chose as test case a circular cylinder with a constant inflowing velocity field. The grid is circular and symmetric. The wall does not moove. I supposed that the result is the same if I let the grid rotate or not, in particular I expected a symmetric flow field. However, if the grid mooves, the flow field is not symmetric any more. The asymmetry is the stronger the larger is the grid speed. I did a benchmark against TascFlow and found a similar result. These calculation were steady state. If I perform transient calculations, this effect occures if the time step is rather large, e.g. if I resolve one grid revolution with less than 10 time steps and the grid velocity is of the same order as the inflow velocity, irrespective if I use the space conservation law or calculate the grid velocities by pure kinematics. What might be the reason, and what other test cases can be recommended? In the following some implementation details:  Absolute, cartesian velocity components as dependent variables  Colocated cellcentred variable arrangement  The only difference to fix grids is the treatment of the convective fluxes, namely a "relative mass flux" for the convective transport is introduced by the grid movement  The Conti or pressure correction equation is kept unchanged,except that the divergence is evaluated by the "relative mass flux"; should have no influence for pure rotation of the circular grid. Thank you very much for any hint!
With best regards from Munich Romuald Skoda 

August 21, 2000, 11:47 
Re: Mooving Grids

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(1). If you rotate the grid at a constant speed, then it becomes very difficult to compute the flow using the fixed frame of reference. (2). If you sit on the rotating frome and write the governing equations on the rotating frame of reference, then the grid will be stationary relative to it. (3). The problem is: rotation is not translation, constant rotation will produce acceleration, while constant translation will not produce acceleration. As a result, the governing equations will be different in the rotating frame of reference. (4). You also need to take care of the relative motion of the boundary conditions, if you are using the rotating frame of reference. (5). If on the other hand, you are using fixed reference frame, then the moving grid is basically a transient flow problem, there will be contributions from the motion of the grid. So, you should be very careful in deriving the governing equations.


August 22, 2000, 00:36 
Re: Mooving Grids

#3 
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is your flow laminar or turbelent


August 22, 2000, 00:55 
Re: Moving Grids

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The test case is laminar (Re=1). In general, I am going to use wall functions later. In response to Dr. Chien: what in particular is the problem about staying in the absolute frame and let the grid move? I chose the absolute frame because I am going to couple the moving domain with a fixed one. By the way: Sorry for the ugly spelling error in "moving"


August 22, 2000, 06:18 
Re: Moving Grids

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The best way to test your implmentation of moving grid is to have no physical flow  in your case use zero inflow velocity. Even better is to use inviscid so you only have convection term to worry about since the grid velocity only affects the convection.
Now use the same case, the mesh movement itself should not create any flow at all (in reality due to numerical precision, you may have velocity in the order of 10E5 or so). 

August 22, 2000, 07:44 
Re: Moving Grids

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I would use the following simple test case: Set up a regular structured grid, let the outer boundaries fixed and then just contract the inner mesh. E.g. x and y components do decrease and then increase again, such that one gets a volume change. (Peric test case) If the fluid is at rest, nothing should happen. If something happens there is something wrong with the implementation of the GCL, I would guess.
Formulating both, the volumes of the cells and grid velocities on geometric quantities of course does give wrong results due to violation of the GCL. (I assume that this is almost not worth mentioning anymore) I would first look for the implementation of the GCL, if that is ok. Frank 

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