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In this paper, we look at the pressure checkerboard problem that arises in anEulerian meshless method that solves the incompressible Navier-Stokes equationsusing the generalized finite difference method (GFDM). Although, thecheckerboard problem has been dealt with extensively in mesh-based methods, theliterature in connection with meshless methods is comparatively scarce. In thispaper, we explore the occurrence of the checkerboard problem in a meshlessmethod. A few unsuccessful attempts to resolve the checkerboard problem arereported. The successful fix for the problem entails an algorithm that adaptsthe point cloud by adding points in the regions of pressure oscillations. Thealgorithm uses an error indicator that detects the presence of the checkerboardoscillations in the solution. The algorithm minimizes the computational effortsince it ensures the use of additional points only in regions of concern, asdirected by the error indicator, in contrast to an approach of using a highlyrefined set of points throughout the domain. It also requires no a prioriestimates of the regions where the oscillations occur and integratesconveniently in the framework of the meshless method since no re-meshingstrategies are involved. The results are compared with literature and a goodmatch is observed.

Addressing the checkerboard problem in an Eulerian meshless method for incompressible flows