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reconstruction. The implicit, first-order LU decomposition scheme is applied to flowfield computations
of underwater bodies with full appendages.

2 GOVERNING EQUATIONS
Artificial compressibility method, which adds a time-derivative of the pressure to the continuity equation
of incompressible Navier-Stokes, can couple the equations of motion with the continuity equation. Then
one can apply the most efficient implicit time-dependant methods to the incompressible Navier-Stokes
equations, i.e. the complete set of governing equation can be solved simultaneously.
The Navier-Stokes equations in conservation law form for an incompressible, three-dimensional flow
are written as

Q, + (E' - + (F' -I?,:),, + (G' -G;): = 0 (1)
E', F',G' are inviscid flux vectors, E:, F,:,Gi are viscous flux vectors ( Peter, et al. 1988).
Following the artificial compressibility method, the dependant variable vector Q in Eq.(l) are defined as

Q = (P, u,v, w)' (2)
Considering a coordinate transformation of the form 5 = g(x,y,z) , q = q(x,y, Z) , and g = S(X,~, Z) ,
Eq.( 1) can be rewitten in strong conversation law form.
(QIJ), +(E-E,); +(F-F,.), +(G-G,,), =O (3)

The flux vectors E,F,G are linear combination of E*,F*,G'in Eq. (1). For example, E can be
written as
E=(<, IJ)E' +(c,IJ)F' +(tz IJ)G' (4)

Where J is the Jacobian of the coordinate transformation.

3 NUMERICALSCHEMES

3.1 High Resolution Schemes for Invkchi Flux
Because of the complicity of the flowfield structure around the underwater bodies with full appendages,
Essentially Nonoscillatory (ENO) schemes, which was developed by Harten et al, are applied in the
numerical simulations of this paper. EN0 schemes, which use adapted stencil, are uniformly high-order
accuracy throughout even at critical points
Following Yang( 1992), third-order nonoscillatory schemes are given below. Take SE, in direction 6
of Eq. (3) as an example, let A = ,(A E , = (A,, &,A,, .I, are eigenvalue diagonal matrix of A.
dQ It-
ft, L are right and left eigenvector matrices of eigenvalue diagonal matrix AE. Then we can get
A = RAE L . The spatial difference of Et can be reached by using finite volume method

EN03 - EENO~
E, = E,+1/2 ,412 (5)