Meshless methods for a simple atmospheric model

Abstract

In this paper, two meshless methods, the "Smoothed Particle Hydrodynamics (SPH)", the "Meshless Local Petrov-Galerkin (MLPG)" and the classical upwind finite difference method (FDM) are applied to a linear one space dimension advection equation with specified periodic boundary condition. In SPH, a cubic spline weight function is used to determine the advection field at the nodes in the support domain. For MLPG method, the weight residual is confined to a very small local sub-domain. The numerical integrations are carried out over a local quadrature domain defined for the node, which can also be the local domain where the test (weight) function is defined. The results from three methods are compared with the corresponding exact solutions.