Quadrature-Free Non-Oscillation Finite Volume Scheme for Solving Navier-Stokes Equations on Unstructured grids

This paper presents a family of high order finite volume schemes for solving Navier-Stokes equations on unstructured grids. The k-exact reconstruction is performed on every control volume as the primary reconstruction. On a cell of interest, besides the primary reconstruction, additional candidate reconstruction polynomials are provided by means of very simple and efficient "secondary" reconstructions. The weighted average procedure of the WENO scheme is then applied to the primary and secondary reconstructions to ensure the shock capturing capability of the scheme. A quadrature-free way is proposed to perform WENO schemes for saving computation. Several test cases are presented to validate the accuracy and non-oscillation property of the proposed schemes.