The numerical modelling of the atmosphere motion with meshfree methods

Neglecting turbulent motion of the atmosphere we consider the Navier–Stokes equations to calculate the wind velocities. We use a Lagrangian discrete vortex method to compute main characteristics of the flow. The core of the vortex method is to find the solution to the Poisson equation. For solving the Poisson equation with Dirichlet and Neumann boundary conditions the Element Free Galerkin (EFG) and the Finite Pointset (FP) methods, as well as a modification of the latter, are examined. It is shown that the EFG method increases the computational speed in comparison with the FP method. It is determined that the grave disadvantage of the FP method is a low-rate convergence while the computational complexity of each iteration is reasonable. The use of the modified FP method shows that the elapsed time is comparable with that of the EFG method although as the problem size increases the advantage of the FP method is not so obvious.