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 Arthur May 2, 2002 17:03

Multi-block

Is it possible to treat the multi block using an iterative manner? Just like feeding the outflow of one block to the other block as an inflow. If it is possible, what is the boundary conditions on the inter-block surface? Thanks

 jing May 3, 2002 03:26

Re: Multi-block

in the multo-block technique, two layer cells are extended out around every block. They are named as virtual cells and dummy cells. They are correspondent with the cells in the neigbouring blocks, which means the virtual cells and dummy cells have the same flow field parameters with the correspondent cells in other block. In the iterative process, the boundary conditions on the inter-block surfaces can therefore be transfered with each other.

 Arthur May 5, 2002 17:39

Re: Multi-block

Thanks for your help. But can you give me more details . For example, for a very simple case, if I devide a backstep into two zones (though this is some kind of unnecessary to use multi-block), and use dummy cells as you said. When I solve for the first zone, what is the boundary condition that I can use for the dummy cells, outflow? And if using an iteritive method, I can use that outflow from zone1 for my second zone and solve the zone2. But what is the next step, how the iterative way continue? Thanks very much.

 jing May 8, 2002 03:24

Re: Multi-block

When you devide a backstep into two zones, the two zones have a common interface. The dummy cells and the virtual cells should be developed around the whole block, including the common interface and other boundaries. At the beginning of the calculation, the flow field in the solution domain should be initialized. The flow field distribiton (or boundary condition) for the dummy cells in the first clok on the common interface should be valued by the distribution in the corresponding cells in the block 2. The flow field distribution for the dummy cells in the first clock on the other boundary are taken from normal boundary conditions. For the block 2, it is same. After the first iteration, revalue the flow field disribution for the dummy cells in the first block on the common interface according to the flow field you obtains in the block 2. For the block 2, it is same. It means you should exchange the data for the dummy cells on the interface in each iteration.

You can also find some documents in the internet which introduce how to exchang data in the multi blocks and paralle calculation.

 Jonas Holdeman May 9, 2002 09:17

Re: Multi-block

Has anyone tried the following procedure?

I am assuming a finite element method using sparce matrix techniques. Assume the blocks have been independently assembled into a global matrix. This global matrix will be block diagonal. Matrix blocks corresponding to two ajoining multi-blocks will each contain partial contributions to degrees of freedom on common the edges.

Assume one has a fast way to solve the individual uncoupled blocks, say by a parallel computation with a separate processor handling each block. The blocks can be coupled by replacing one column of the set of common DOFs (a pair if the DOF is on an edge, more if on a common corner of several blocks) by the sum of the columns from different blocks and the rows by the sum of the rows from different blocks. The remaining rows and columns are replaced by zeros except for a 1 on the diagonals and a -1 in the summed column (a simple change can make this symmetrical). The RHS would be modified as well. This procedure completes the assembly of one of the common DOFs and constrains the remaining common DOFs to be equal.

This modification of the global matrix is of the form so that the Woodbury formula (a generalization of the Sherman-Morrison formula for updating the solution or inverse of a matrix if one matrix element is changed-- see "Numerical Recipes in C/C++/Fortran/etc") can be used to find the (correct) coupled solution from uncoupled solutions using the fast (parallel) block solvers.

I suppose this could be used iteratively, turning on and off the coupling between pairs of blocks.

I would appreciate a thoughtful critique or references if anyone has seen this done.

 Arthur May 12, 2002 22:25

Re: Multi-block

Can I do it in this way: I get the velocity at the interface, and use it as inflow for the second zone. After generating the pressure distribution in second zone, I put the pressure on the common boundary and compute the flow in first zone again, so iteration keeps on. It seems ok since the result is very close to that of FLUENT, but is there problem for such scheme? Thanks very much.

 Jing May 15, 2002 11:02

Re: Multi-block

It seems Ok to exhange the data in this way. If the data contained in the boundary conditions are enough for the calculation in the second block, it should work too.

 Jing May 15, 2002 11:12

Re: Multi-block

Sorry,I forget one point. With your method, as the flowfield on the interface in the first block is taken as the inflow of the second block, the corresponding cells near the interfaces in the two blocks have the same flowfield. Theoretically, it is not right. Since continuity property is expected on the interface, not the equal flow field. But you can taken it as a coarse numerical algorithm, no problem.

 Arthur May 20, 2002 16:51

Re: Multi-block

Thanks. Since I am using finite volume method and matched grid, the same velocity distribution can satisfy continuity, do you think so? And I am not clear some points in your reply in 8th, May. 1. Why dummy cells are all around the domain, are they computed besides the cells around interfaces? 2. How do you start compute zone2 for the back step case? Because the inflow face for this zone is the interface, how do you decide the inflow for this zone? And can you recommend me a more detailed paper for such kind of multiblock manipulations? Thanks very much

 Jing May 27, 2002 05:44

Re: Multi-block

It is not so easy to explain it only with text. And I don't have a right paper just on hand. Please search in the Internet with the key words "multi-block" or "Message passing library". You will find enough useful information.

Good Luck!

Jing

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