  In this paper, a simple and efficient third-order weighted essentially
non-oscillatory (WENO) reconstruction is developed for three-dimensional flows,
in which the idea of two-dimensional WENO-AO scheme on unstructured meshes
\cite{WENO-ao-3} is adopted. In the classical finite volume type WENO schemes,
the linear weights for the candidate stencils are obtained by solving linear
systems at Gaussian quadrature points of cell interface. For the
three-dimensional scheme, such operations at twenty-four Gaussian quadrature
points of a hexahedron would reduce the efficiency greatly, especially for the
moving-mesh computation. Another drawback of classical WENO schemes is the
appearance of negative weights with irregular local topology, which affect the
robustness of spatial reconstruction. In such three-dimensional WENO-AO scheme,
a simple strategy of selecting big stencil and sub-stencils for reconstruction
is proposed. With the reconstructed quadratic polynomial from big stencil and
linear polynomials from sub-stencils, the linear weights are chosen as positive
numbers with the requirement that their sum equals one and be independent of
local mesh topology. With such WENO reconstruction, a high-order gas-kinetic
scheme (HGKS) is developed for both three-dimensional inviscid and viscous
flows. Taken the grid velocity into account, the scheme is extended into the
moving-mesh computation as well. Numerical results are provided to illustrate
the good performance of such new finite volume WENO schemes. In the future,
such WENO reconstruction will be extended to the unstructured meshes.
