High-order fluxes for conservative skew-symmetric-like schemes in structured meshes: Application to compressible flows

Developing high-order non-dissipative schemes is an important research task for both steady and unsteady how computations. We take as a starting point the "built-in" de-aliasing property of the discretized skew-symmetric form for the non-linear terms of the Navier-Stokes equations, recalled in Kravc henko and Moin [1]. Two families of high-order locally conservative schemes matching this discretized skew-symmetric form are considered and rewritten in terms of telescopic fluxes for both finite difference and finite volume approximations in the context of compressible hows. The Jameson's scheme [ 2] is shown to be the second-order member of larger families of "skew-symme tric-like" centered schemes. The fourth-order finite volume and finite diff erence and the sixth-order finite difference schemes which belong to this f amily are provided. The proposed schemes are extended to shock capturing sc hemes, either by modifying the Jameson's artificial viscosity or by hybridi ng the centered flux with Weno [3] fluxes. An adapted interpolation is prop osed to extend the use of the proposed schemes to non-regular grids. Severa l tests are provided, showing that the conjectured order is properly recove red, even with irregular meshes and that the shock capturing properties all ow us to improve the second-order results for standard test cases. The impr ovement due to fourth-order is then confirmed for the estimation of the gro wth of two- (TS waves) and three- (Crow instability) dimensional unstable m odes for both confined and free-shear hows. The last application concerns t he steady computation using the Spalart-Allmaras model of a separated bound ary layer: it confirms that the use of a high-order scheme improves the res ults, even in this type of steady applications. (C) 2000 Academic Press.