DETERMINATION OF SOME SOLUTIONS OF THE STATIONARY 2D NAVIER-STOKES EQUATIONS
| Autor: | BALTAG, Iurie |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
stationary two-dimensional navier-stokes equations
system of equations with partial derivatives exact solutions method of separation of variables viscosity pressure velocity of plane flow of a liquid or gas Engineering (General). Civil engineering (General) TA1-2040 Electronic computers. Computer science QA75.5-76.95 |
| Zdroj: | Journal of Engineering Science (Chişinău), Vol XXIX, Iss 4, Pp 38-50 (2022) |
| Druh dokumentu: | article |
| ISSN: | 2587-3474 2587-3482 |
| DOI: | 10.52326/jes.utm.2022.29(4).03 |
| Popis: | In this paper, various solutions of the stationary Navier-Stokes equations, which describe the planar flow of an incompressible liquid (or gas), are determined, i.e., solutions containing the components of the velocity of flow - the functions u, v and the created pressure - P. The paper contains three proven theorems, as well as various examples and particular examined cases. Applying Theorem 1, we can find various solutions, where the velocity components represent the imaginary and real parts of a differentiable function of a complex variable. Theorem 2 allows us to determine solutions, where the velocity components are expressed by the partial derivatives of the solutions of Laplace's equation of a special form. It is to be mentioned that these theorems give us solutions that do not depend on the viscosity parameter λ. In theorem 3, an original method for obtaining a series of solutions of the Navier-Stokes equations is presented, in which the viscosity coefficient λ participates explicitly; these solutions cannot be obtained by applying Theorems 1 or 2. The paper contains a large number of particular cases examined and examples of exact determined solutions. |
| Databáze: | Directory of Open Access Journals |
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