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Finite-volume compact schemes on staggered grids. (English) Zbl 1106.76406
Summary: Compact finite-difference schemes have been recently used in several Direct Numerical Simulations of turbulent flows, since they can achieve high-order accuracy and high resolution without exceedingly increasing the size of the computational stencil. The development of compact finite-volume schemes is more involved, due to the appearance of surface and volume integrals. While J. M. C. Pereira et al. [J. Comput. Phys. 167, No. 1, 217–243 (2001; Zbl 1013.76054)] and Smirnov et al. [AIAA Paper, 2546, 2001] focused on collocated grids, in this paper we use the staggered grid arrangement. Compact schemes can be tuned to achieve very high resolution for a given formal order of accuracy. We develop and test high-resolution schemes by following a procedure proposed by S. K. Lele [J. Comput. Phys. 103, No. 1, 16–42 (1992; Zbl 0759.65006)] which, to the best of our knowledge, has not yet been applied to compact finite-volume methods on staggered grids. Results from several one- and two-dimensional simulations for the scalar transport and Navier–Stokes equations are presented, showing that the proposed method is capable to accurately reproduce complex steady and unsteady flows.
76M12Finite volume methods (fluid mechanics)
76D05Navier-Stokes equations (fluid dynamics)