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Treatment of Edges (boundary Condition)-- Help

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Old   March 31, 2010, 05:27
Default Treatment of Edges (boundary Condition)-- Help
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zhwan
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Hi, all

I am writing a DRP code to compute the aeroacoustics. But I don't know how to implement the edge boundary condition ( isothermal).

viscous wall. (U=V=0,T=const)
____________ edge
|
| viscous wall ( U=V=0, T=const)
|
schematic figure.

I used the treatment introduced by T.J. Poinsot. & S.K. Lele.
JCP101,104-129(1992). However, it will cause numerical instability. I don't know why,...
Here is the steps of my treatment:
1. compute the L5 both in x direction and y .
L5 = lambda_5 * (dp/dx + rho * ar * du/dx) ( x--direction)
i = 0 i = 1 i=2
#---#----#----#
| edge
#
dpx =( p_{i=2}-p_{i=1})/dx, the same for du/dx

2. Set L1= L5, L2=L3=0, then we can get d1,d2,d3,and d4
3. Integrate
d{rho}/dt + d1_x + d1_y = 0
4. After getting density, use it to compute the Pressure.

Does anyone have any idea which step is wrong? or is there any other method used to implement the isothermal wall-edge condition for aero-acoustic computation.
Thanks advance.

zhwan
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