Numerical recipes: the art of scientific computing
Numerical recipes: the art of scientific computing
An improvement of fractional step methods for the incompressible Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
On the direct solution of Poisson's equation on a non-uniform grid
Journal of Computational Physics
Fully conservative higher order finite difference schemes for incompressible flow
Journal of Computational Physics
On a class of Padé finite volume methods
Journal of Computational Physics
High order finite difference schemes on non-uniform meshes with good conversation properties
Journal of Computational Physics
A robust high-order compact method for large eddy simulation
Journal of Computational Physics
High Order Accurate Solution of Flow Past a Circular Cylinder
Journal of Scientific Computing
Compact finite volume schemes on boundary-fitted grids
Journal of Computational Physics
Journal of Computational Physics
Curvilinear finite-volume schemes using high-order compact interpolation
Journal of Computational Physics
Journal of Computational Physics
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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 revolved, due to the appearance of surface and volume integrals. While Pereira et al. [J. Comput. Phys. 167 (2001)] 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 Lele [J. Comput. Phys. 103 (1992)] 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.