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In this paper, a simple and efficient third-order weighted essentiallynon-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 linearsystems at Gaussian quadrature points of cell interface. For thethree-dimensional scheme, such operations at twenty-four Gaussian quadraturepoints of a hexahedron would reduce the efficiency greatly, especially for themoving-mesh computation. Another drawback of classical WENO schemes is theappearance of negative weights with irregular local topology, which affect therobustness of spatial reconstruction. In such three-dimensional WENO-AO scheme,a simple strategy of selecting big stencil and sub-stencils for reconstructionis proposed. With the reconstructed quadratic polynomial from big stencil andlinear polynomials from sub-stencils, the linear weights are chosen as positivenumbers with the requirement that their sum equals one and be independent oflocal mesh topology. With such WENO reconstruction, a high-order gas-kineticscheme (HGKS) is developed for both three-dimensional inviscid and viscousflows. Taken the grid velocity into account, the scheme is extended into themoving-mesh computation as well. Numerical results are provided to illustratethe good performance of such new finite volume WENO schemes. In the future,such WENO reconstruction will be extended to the unstructured meshes.

High-order gas-kinetic scheme with three-dimensional WENO reconstruction for the Euler and Navier-Stokes solutions