Chapman-Enskog Analysis (Ladd's Numerical Simulations of Particulate Suspensions & Latt's Hydrodynamic Limits)

[anoncarter]

Hi, all!
I’m having a hard time with the Chapman-Enskog analysis, at the point where you use the Euler Equations to rewrite time derivatives as spatial derivatives. In particular, I am reading Ladd’s 1994 Paper, where in Eq. (2.27) the time derivative needs to be eliminated from the following expression

d[sub]t[/sub]( rho c[sub]s[/sub][sup]2[/sup] d[sub]a,b[/sub] + rho u[sub]a[/sub] u[sub]b[/sub] )

I cannot seem to achieve this.

Similarly, Latt’s Thesis deals with the same term [quote=Latt]
d[sub]t[/sub] ( rho u u ),
[/quote]
in Eq. (2.64) on page 25 and somehow eliminates the time derivative.
Again, I cannot see why this equation holds.

[anoncarter]

In a paper by Hou et al. '94, I have now found the same trick used explicitly. So, problem solved.