ANALYSIS OF STABILITY AND CONVERGENCE OF A MODIFIED THREE-STEP SPLITTING SCHEME FOR NAVIER-STOKES EQUATIONS
Zhumagulov B. Temirbekov N. Tamabay D.
2025Institute of Applied Mathematics of Baku State University
Applied and Computational Mathematics
2025#24Issue 3486 - 509 pp.
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.
Atmospheric Boundary Layer Model , Navier-Stokes Equations , Physical Processes , Splitting , Stability and Convergence , “Large Particles” Method
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National Engineering Academy of the Republic of Kazakhstan, Bogenbai Batyr Str. 80, Almaty, 050010, Kazakhstan
Faculty of Mechanics and Mathematics, Al-Farabi Kazakh National University, Al-Farabi Ave., 71, Almaty, 050040, Kazakhstan
National Engineering Academy of the Republic of Kazakhstan
Faculty of Mechanics and Mathematics
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