sci.physics.computational.fluid-dynamics

Hi All,

I wonder if anyone can explain the following.

Plane channel DNS is now standard tool and the most common
method is based on using Fourier for the periodic directions
and Chebyshev tau for the inhomogeneous.

The actual formulation of the equations of motion that I use
is based on the well known omega-phi method (JFM v.177 1987 p133)
where a 4th order for the normal velocity and normal vorticity
are used - the question also arises in influence matrix method.

The solution of the method is based on inverting a standard 1D
equation (using Cheb tau)

f'' - k*k*f = RHS where k*k ~ 2Re/dt

with an analytical solution

f = A*sinh(k*y) + B*cosh(k*y) + Particular_Integral

For a typical low Re DNS k*k ~ 2*5000/0.001 = 10**7

The exponents in the sinh and cosh near the walls are large
typically ~exp(1000).

This represents a very steep near-wall rise. The question
is: Are the 129 Cheb polynomials typically used enough
for resolving such a boundary effect? My tests suggest no.

Is there anything else in this method?

Thanks to anyone who cares to answer.
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