Page 457 - Practical Design Ships and Floating Structures

432
H = iH(<, + jH,,, + kH(,,
1
H =E---,.
(51 Re
HI,, = F--E.
1
Re
1
=
H,,, G - --G,
Re
If Eq.(19) is applied over a hexahedral cell( A{=Aq=Ag = I), time discretion uses first -order-accurate
differencing, inviscid terms use implicit difference, viscous terms are explicit central difference. we can
rewrite Eq. (3) as
J-' (e,'::' - Q,"' ) + A,([ E,':',? - E,::: I + [F,'J!,, - F,'-::: 1 + [G;:*:/l - 11
At I,
= -{[K.,+1/2 -E,*:,,,] + [E.:,,,, - E:-1/2 1 +[GvI+112 - G":-1/211 (21)
Re
The definition of (AE),+l,2 and A = (dE/ZQ),+l,2 are same as last section. Let

If L, . R, are the left and right eigenvector matrices of matrix A, we can get

A' = R,Ai.LE
Similarly
B* = R, A:.L,

3.3 Turbulence Model

The effect of turbulence fluctuations, which can be resolved on the computational grid, are approximated
with the Smagorinsky model.
PI = (c,L)21S,fI (25)

in which the model coefficient C,s = 0.1 and length scale is the geometric mean of the grid spacing
L = (AxAyAz)"'.