On a Conservative Solution to Checkerboarding: Examining the Discrete Laplacian Kernel Using Mesh Connectivity

CFD codes that are used for industrial applications commonly use a collocated grid arrangement to calculate the physical flow variables. When using a central differencing gradient (CDG) to discretise the continuous operators of the Navier-Stokes equations, a wide stencil is obtained for the Laplacian operator. This wide stencil, in turn, leads to a decoupling between odd and even grid points of the pressure field that results from the pressure Poisson equation. This decoupling can lead to non-physical, spurious modes in the solution, a problem commonly known as the checkerboard problem (Ferziger et al., 2002).