Positivity preservation, stencil selection and applications of LSKUM to 3-D inviscid flows

Abstract

Meshless methods do not require a mesh but only need a distribution of points in the computational domain. At any point, the approximation of spatial derivatives appearing in the partial differential equations is performed using a local cloud of points called the connectivity (or stencil). While point generation is easier than mesh generation, the selection of a good stencil becomes critical to the success of meshless methods. In this work we develop some criteria for quantifying the quality of stencils for meshless methods and apply them to LSKUM using points obtained from a complex grid system called FAME. We also show that LSKUM is positivity preserving under a CFL condition which lends further evidence to its robustness.