Numerical modeling of air mass motion by the mesh-free method

The Navier-Stokes equation, applied to the calculation of wind velocity without accounting for the turbulent motion of the atmosphere, is considered in this work. The main flow characteristics were computed with the use of the Lagrange discrete vortex method for finding the solution of the Poisson equation under the Dirichlet and Neumann boundary conditions. To do this, two mesh-free methods: the element-free Galerkin (EFG) and the Finite Pointset (FP) methods, as well as the modification of the latter, have been analyzed. It is shown that the computation speed of the EFG method is higher than of the FP-method. It is determined that a serious disadvantage of the FP-method is its low rate convergence, while the computational complexity of each iteration is reasonable. The use of the modified FP-method has shown its computational speed to be comparable with that of the EFG method, although the advantage of the FP-method is not obvious when the size of the problem increases. © 2009, Pleiades Publishing, Ltd.