Numerical applications and developments of finite volume compactschemes on staggered grids

Compact finite-difference schemes have been recently used in several Direct Numerical Simulations of turbulent flows, in order to achieve high-order accuracy and high resolution. The development of compact finite-volume schemes is more involved, due to the appearance of surface and volume integrals. In this paper we select a staggered grid arrangement, whose good characteristics are advantageous in the simulation of incompressible flows. Compact schemes can be tuned to achieve very high resolution, for a given formal order of accuracy. In this respect, we develop and test high-resolution schemes by following a procedure first introduced by Lele (1992, J. Comp. Phys., 103). Numerical evidence of the good characteristics of the developed method is presented.