Hi,
While simulating flow in a rectangular channel and using primitve variable formulation, what should be my pressure gradient boundary condition at outlet where I have assumed fully developed flow, ( the length of the channel is large enough).
For velocity, I have du/dx=0, and v=0;
For dp/dx= -12/Re and dp/dy=0.
Is this correct.
I have been looking for papers on artificial compressibility method or any other primitive variable formulation, where people have used pressure gradient as dependent variable and solved for pressure gradient in flow across a channel.
Also, I am using FDM method to solve NS equation. At the outlet, I need to discretize diffusion term using second order scheme. One sided formulation is what I am implementing
Refer this link:https://himech.files.wordpress.com/2010/02/ch08.pdf
Refer this link:https://www.uio.no/studier/emner/matnat/math/.../Pipeflow_intro.pdf
Refer this link:www.fem.unicamp.br/.../FULLY_DEVELOPED/FULLY_DEVELOPED
Normally the pressure boundary condition at the outlet of a fully developed channel is given by prescribing a constant normal stress at the outlet i.e. -p + 2*mu* du/dx = Constt. The constant could be Zero as well. And in non-dimensional form the, the BC would be. –p + 2/Re*du/dx = 0 where Re = HU/nu and H is the height of the channel. Since the flow is fully developed, du/dx = 0, So the pressure p = 0 at the outflow. So should you try dp/dx = 0??? (see the ref. below).
Gartling, D, “ A test problem for outflow boundary conditions – flow over a backward facing step”, International Journal for Numerical Methods in Fluids, V11, pp 953 – 967, 1990.
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