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dirichelet boundary conditions for hyperbolic problem |
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August 9, 2015, 06:59 |
dirichelet boundary conditions for hyperbolic problem
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#1 |
Senior Member
Join Date: Jun 2010
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Hi,
I am solving a set of 1D hyperbolic equation for a variable density flow. So far I have been using averaging to discretise p and v at the boundary. At the boundaries I have been using linear extrapolation to p and v at the left and right boundaries. For instance, for velocity at the left boundary I have used vw = v(1) - 2*v(2) where v(1) and v(2) represent the first and second nodes from the left boundary. To impose the Dirichlet boundary conditions, I have either just set vw = BC or vw = BC - 2*v(2) I think this is what is the virtual node approach (?) The problem I have with this method is that as I increase my number of nodes I get alot of fluctuations as if a wave reaches the boundary and is reflected back. I am looking for an easy fix to the problem. I tried using up-winding but still have the same problem. Please help if this is your area of expertise. Thank you in advance |
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August 9, 2015, 08:05 |
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#2 | |
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Filippo Maria Denaro
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Quote:
If you have Dirichlet B.C.s you need just to set values at one boundary, in your case the left one. I don't understand why you want to use extrapolation...no ghost points are needed |
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August 9, 2015, 08:14 |
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#3 |
Senior Member
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Hi,
Thank you, that is what I had done originally but it caused fluctuations at the boundary. Therefore, after searching literature I found virtual nodes, and like you said it did not help. If I did not have a Dirichlet BC, and I just needed to define the left boundary would it be correct to use the extrapolation? I am in particular, having problems with my pressure BC, I have come across some papers where they simply use pw = p(1) or pe = p(end) |
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August 9, 2015, 08:31 |
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#4 | |
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Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,863
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Quote:
no, for hyperbolic equations the BC.s are dictated by the direction of the characteristic lines. Thus, extrapolation at the left boundary can be used only if you have a wave coming from the interior and going toward the left boundary. If you have Euler equation and subsonic flows, you have 2 characteristics coming from the left boundary and going into the interior and 2 Dirichlet conditions are required, 1 characteristic is from the interior and you can use extrapolation for that condition. If your flow is supersonic the 3 characteristics require 3 Dirichlet BC.s |
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August 12, 2015, 18:26 |
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#5 |
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Thank you.
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boundary condition, dirichlet, discretization, extrapolation, hyperbolic |
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