Analysis of stability and convergence of a modified three-step splitting scheme for Navier-Stokes equations (pp.486-509)

The article presents numerical solution for the Navier-Stokes equations and the atmospheric boundary layer equations using a modified difference splitting scheme.It examines the widely used the Marker-and-Cell (MAC) method and evaluates its effectiveness.The study investigates stability and convergence within the "large particles" method, emphasizing a threestep splitting scheme.Research provides a priori estimates for the second derivative of velocity and pressure gradient.Proposed method computes auxiliary velocity fields at boundary nodes and solves a pressure equation, differing from techniques using Neumann conditions, which may not reflect the physical problem.Numerical simulations are performed for convective flow in a rectangular cavity.A numerical comparison is conducted between the classical two-step splitting method and the modified three-step scheme.Method's applicability is shown through modeling pollutant dispersion in the atmosphere of an industrial city.