In hydrodynamic calculations, the confederation of the right set of coordinates of a continuous medium (gas, liquid) becomes complicated because it makes the calculation mechanismspecific and tied only to a specific object. The paper is devoted to an improved method to calculate the small-scale circulation of the surface layer of the atmosphere in urban areas with many isolated buildings from each other. The proposed method will work for explicit and implicit schemes for calculating the transport equations and conservation of momentum of motion. It is designed to calculate the small-scale circulation of the surface layer of the atmosphere in urban areas with many isolated buildings from each other. The method allows for consideration of the interaction of a continuous medium flow with impenetrable obstacles discretely and randomly located inside the calculation area. This method will be helpful when calculating microcirculation in urban development.
The finite-difference scheme of directed differences (the Courant-Isaacson-Ries scheme), which is widely used in the practice of aerohydrodynamic calculations, is studied theoretically and on the example of test problems. We applied the commonly used in practice Courant-Isakson-Ries directional difference scheme that allowed us to find and show distributions of velocities where the laws of the matter conservation are violated in the calculations in solving the matter conservation equations or the correspondence of the obtained solutions to the most general practical understandings on the essence of the matter transfer. A scheme free from the shortcomings of the Courant-Isaacson-Ries scheme has been constructed, tested, and proposed for use in aerohydrodynamic calculations by the finite difference method. Moreover, all the valuable properties of this well-known scheme are preserved. Among the maintained properties: are transportability, conservatism, stability in calculations, invariance, and adequacy of the essence of the physical phenomenon of the transfer of matter in space. The disadvantages of the new finite-difference scheme proposed for solving the equations of conservation of matter should be considered: an increase in the required RAM for storing electronic means of calculating information about the velocity field in memory and an increase in the number of calculations needed.
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