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Old   January 12, 2001, 07:06
Default Stream function
Cauvery G
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Hi Everybody,

Can someone tell me how to find the streamfunction values from the discrete values of velocity components

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Old   January 12, 2001, 10:58
Default Re: Stream function
Posts: n/a
Hi G,

because rot ( streamfunction ) = velocity, I started this way:
find the streamfunkton, which minimises ( integral ( rot ( streamfunction ) - velocity ) ^2 )
the usual(?) procedure gives the euler-lagrange-pde:
solve rot ( rot ( streamfunktion ) ) = rot ( velocity )
rot ( velocity ) is also known as vorticity
rot ( rot (x) ) is similiar to the Laplacian, but be careful when working with other than cartesian coordinates (eg cylinder coordinates)
if you are using finite elements, you can shift one rot-operator to the test function
the rot operator (or rotation or curl) should be found in each book about mathematics for engineers
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Old   January 12, 2001, 13:39
Default Re: Stream function
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Laplacian (stream function) = - vorticity for an incompressible, constant density flow.

Vorticity can be easily computed from the velocity field. Stream function is obtained upon solving the above Poisson equation.
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Old   January 13, 2001, 21:10
Default Re: Stream function
John C. Chien
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(1). In 2-D flow, it is possible to define the stream function from the velocity field. For example, d(psi)/dy=rho*u, d(psi)/dx=-rho*v, will satisfy the continuity equation automatically. (2). You can then find the stream function, psi distribution from the integration of the definition, given above. (3). To get more accurate stream function distribution, you may have to first curve fit the velocity field and use it in the integration. (4). The other approach is to solve the stream function equation, with the vorticity as the source term (which can be derived from the velocity field through the vorticity definition). This requires programming and will be more involved than the simple integration method.
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