Computing Flow on General Two-Dimensional Nonsmooth Staggered Grids

The classical staggered scheme for the incompressible Navier-Stokes equations is generalized from Cartesian grids to general boundary-fitted structured grids. The resulting discretization is coordinate-invariant. The unknowns are the pressure and the contravariant volume flux components. The grid can be strongly nonuniform and nonorthogonal. The smoothness properties of the coordinate mapping are carefully taken into account. As a result, the accuracy on rough grids is found to be at least as good as for typical finite element and nonstaggered finite volume schemes. Extension to compressible flows results in a scheme with Mach-uniform accuracy and efficiency for Mach numbers ranging from M = 0 to M > 1. Accurate discretization of two-equation turbulence models is also possible.

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