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Old   November 26, 2001, 06:36
Default FDM
Emad Khalifa
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I'm using a new Finite difference method by Strikwerda.

The method is 2nd order in space and time and has schon good results with laminar flow test cases. The uses non staggered grid and solves the conti. and momentum eqns. simultaneously with an iterative solver (implicit). ---------------------------------------------

I'm trying to use the scheme to simulate fully developed turbulent pipe flow in cylindrical coordinates.

At the inlet and outlet of the pipe I use periodic boundary and wall boundary at the wall of the pipe. The pressure is calculated with extrapolation at all boundaries. --------------------------------------------- And I have a question concerning the Boundary condition at the middle of the pipe. At the middle of the pipe there exists a singularity because of the finite difference method used. This means I have to implement an artificial boundary condition.

I use Neumann boundary conditions for velocities ( The gradient of velocities perpindicular to this boundary is zero) Does any one have any other suggestion ??

Thank You

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Old   November 26, 2001, 13:23
Default Re: FDM
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The radial velocity gradients are not zero at the centerline in turbulent pipe flows. It is hard to deal with the centerline singularity using non-staggered meshes. To my knowledge, there isn't an elegant solution to this problem.

Take a look at paper by Verzicco and Orlandi in JCP (95-97 time frame). This is a paper on staggered schemes but you might get some ideas from it. If you resolve this problem, it would greatly be appreciated by many if you can share it with us here.
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