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Question about N-S eqs. in body fixed noninertial reference frame

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Old   July 12, 2011, 18:07
Default Question about N-S eqs. in body fixed noninertial reference frame
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Hi, all

I am writing a N-S eqs. solver to solve oscillating cylinder in quiescent water.

I figured out N-S eqs in noninertial reference frame and the frame is fixed on the center of the cylinder and moving with the cylinder. In this case, translational vector appears in the form of source at the right hand side of the N-S equation.

My thinking is, once the governing equations are described in noninertial reference frame moving with the body, it is not necessary to deform the initial mesh according to the motion of the body.And the outer boundary condition will change with the motion of noninertial reference frame. Is it right?

the translational vector xa is defined by xa = -A sin(2*pi*f0*t) where A is amplitude of the oscilation, and f0 is frequency.

At this point, boundary condition at the inlet, outlet is differ from that of inertial reference frame.

since u = dxadt + ur where u is velocity in inertial reference frame and ur in noninertial reference frame, and dxadt is translational velocity,
then inlet boundary condition becomes
ur = (u_inf - dxadt )_{inlet boundary} --(1)
where u_inf is inlet velocity at infinity in inertial reference frame.

however, I cannot figure out how the outlet boundary condition will be, and instead giving dirichlet type like eq. (1), is it better to give neumann type? if so, how can I formulate the condition?
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