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March 25, 2015, 16:57 |
About the flux in FVM
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#1 |
Member
Tommy Chen
Join Date: Mar 2011
Location: University of Michigan
Posts: 96
Rep Power: 15 |
Currently I am reading some example code of 1D euler equation with FVM.
I wonder is that in FVM, the state at the boundary of a cell should be equal to the center value ? or it has to be interpolate using a slope computed by neighbored cells so that it is not equal to the cell center? |
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March 25, 2015, 17:03 |
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#2 | |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,832
Rep Power: 73 |
Quote:
the time update is provided in terms of volume average, therefore you have to expresse a functional relation between average and pointwise value for computing the flux. For example, the Burgers equation is solved for the average u_bar but the flux is u^2/2. Therefore you need a reconstruction u=u(u_bar). Assuming u=u_bar in the center of the FV is a second order accurate reconstruction. Higher order reconstruction is more complex |
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March 25, 2015, 17:07 |
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#3 | |
Member
Tommy Chen
Join Date: Mar 2011
Location: University of Michigan
Posts: 96
Rep Power: 15 |
Quote:
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March 25, 2015, 17:12 |
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#4 |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,832
Rep Power: 73 |
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March 25, 2015, 21:44 |
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#5 |
Member
Tommy Chen
Join Date: Mar 2011
Location: University of Michigan
Posts: 96
Rep Power: 15 |
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March 26, 2015, 16:36 |
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#6 |
Senior Member
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Also consider that u=u_bar is second order in the cell center only. If, on a cell face, you compute the velocity as u_f = u_bar (the average value in the cell), you ar at most first order accurate. If you pick the wrong cell for such interpolation (i.e., downwind) you are not even first order.
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