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January 19, 2018, 11:29 |
Versteeg Example Question
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#1 |
New Member
Karla
Join Date: Dec 2017
Posts: 7
Rep Power: 8 |
Dear all,
I am working on the example 5.1 of the Versteeg book (page 137-138). I am specifically looking at the central difference scheme. My question is: why are the boundary conditions for D_A and D_B = 2*\Gamma/delta x= 2*D? Why the "2" and not just D_A=D_B=\Gamma/\delta x=D? I don't understand where the 2 comes from. Thanks. |
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January 19, 2018, 12:16 |
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#2 |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,771
Rep Power: 71 |
Sorry but in my version of the texbook the example 5.1 is at page 106 and solves the 1D linear advection-diffusion differential equation, is that the problem you are solving?
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January 19, 2018, 12:55 |
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#3 |
Senior Member
Join Date: Dec 2017
Posts: 153
Rep Power: 8 |
Hello,
If you are dealing with the diffusion, then the 2 comes from the fact that the cv center of the boundary cell is at distance dx/2 from the center of the boundary face (for a cartesian grid). Thus diffusive flux read Area*(phi_b-phi_C)/(dx/2). After simple algebra, you get what you are looking for. |
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January 19, 2018, 13:44 |
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#4 | |
New Member
Karla
Join Date: Dec 2017
Posts: 7
Rep Power: 8 |
Quote:
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