Abstract
This paper is devoted to the construction and investigation of difference schemes for equations describing the motion of a viscous incompressible fluid in natural “velocity vector - pressure” variables. Much attention is paid to the implicit difference iterative schemes developed on the basis of the idea of “weak compressibility”.
Mathematical problems arising when studying the motion of a viscous incompressible fluid are of current importance both in the theoretical plan and in the study of specific models used in mechanics, physics, and other natural sciences to describe real processes. The processes associated with the flow of a viscous incompressible fluid are successfully described by the Navier-Stokes equations. These systems of equations are nonlinear, do not belong to the evolutionary Cauchy-Kovalevskaya type. The absence of a boundary condition for the pressure on the solid walls of the region under consideration, where the values for the velocity vector components and the small parameter for the higher derivatives are given also lead to technological difficulties. These circumstances certainly complicate the search for analytical solutions of such systems of equations, and with the current state of mathematics they can be solved only by computational methods.
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Yergaliyev, Y., Madiyarov, M. (2019). Implicit Iterative Schemes for Solving Stationary Problems of an Incompressible Fluid with a Large Margin of Stability. In: Shokin, Y., Shaimardanov, Z. (eds) Computational and Information Technologies in Science, Engineering and Education. CITech 2018. Communications in Computer and Information Science, vol 998. Springer, Cham. https://doi.org/10.1007/978-3-030-12203-4_21
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