Vol. 37 No. 3 (2026): July - September
2026-09-30
Open Access

Solution of Hydrodynamic Problems Using a Universal Conservative Scheme for Transport of Conservative Admixtures Coupled with an Algorithm for Solving the Navier--Stokes Equations

M.M. Mirsaidov
A.G. Savitsky
A.T. Salokhiddinov

Received: 2026-10-13

Published: 2026-09-30

PDF (Russian)

Abstract

An algorithm for computational hydromechanics is presented that combines an absolutely conservative transport scheme for momentum and admixtures with explicit finite-difference approximations. The study addresses key difficulties encountered when solving the full Navier--Stokes equations, including loss of conservation in certain schemes, the lack of a separate evolution equation for hydrodynamic pressure, and numerical instability. A cylindrical-coordinate formulation is described using the TIIAME conservative transport scheme together with a derived pressure evolution equation. Interactions between gas components accompanied by exothermic heat release are examined, including their effects on velocity, pressure, temperature and constituent transport. The test calculation produced stable flow fields consistent with conservation laws and physically expected distributions. No comparison with experimental measurements was performed; the assessment of the algorithm relies on numerical stability and the qualitative behaviour of computed fields. The proposed approach may be useful for a wide range of hydrodynamic problems and can be implemented using accessible computational tools.

Keywords

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About the Authors

M.M. Mirsaidov
theormir@mail.ru
National Research University “Tashkent Institute of Irrigation and Agricultural Mechanization Engineers”
A.G. Savitsky
theormir@mail.ru
National Research University “Tashkent Institute of Irrigation and Agricultural Mechanization Engineers”
A.T. Salokhiddinov
theormir@mail.ru
National Research University “Tashkent Institute of Irrigation and Agricultural Mechanization Engineers”

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How to Cite

Solution of Hydrodynamic Problems Using a Universal Conservative Scheme for Transport of Conservative Admixtures Coupled with an Algorithm for Solving the Navier--Stokes Equations. (2026). Uzbek Journal “Problems of Mechanics”, 37(3). https://www.pmjournal.uz/jour/article/view/22

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