Computing flows on general two-dimensional nonsmooth staggered grids

Colocated schemes for the incompressible Navier-Stokes equations on non-smooth grids for two-dimensional problems

“…The PI method is described in References [5,6] for a staggered scheme. In Reference [4], one finds the adaptations required for the colocated approach.…”

“…This is not a trivial matter because, due to the piecewise bilinearity of the co-ordinate mapping, geometric terms such as g and a (h) are discontinuous at the cell faces. This is discussed in detail in Reference [6]. Three methods will be considered here.…”

“…A uniform grid is given in G. The mapping x = x(¨) is assumed to be given in the nodes of G, and extended to all of G by piecewise bilinear interpolation; for details see [6]. This makes the mapping x =x(¨) piecewise differentiable, so that strongly non-uniform grids are allowed.…”

“…The first method (called the BI method for short) used bilinear interpolation. The second (called the PI method) uses the path -integral method described in [4][5][6]. The third (called the AUX method) uses auxiliary points, and is a generalization of a method proposed in [7].…”

A conservative pressure‐correction method for the Euler and ideal MHD equations at all speeds

“…This is based on the general (mis)conception that staggered schemes are inherently less accurate and robust for fully compressible ow than colocated schemes and that staggered discretization in general co-ordinates is inaccurate. However, in References [13][14][15][16] a staggered scheme for the Euler and Navier-Stokes equations is presented that is accurate on non-smooth non-orthogonal grids.…”