K. N. Volkov

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The paper deals with an approach to finite volume discretization of unsteady Navier-Stokes equations on unstructured meshes, and its advantages and development prospects are discussed. Features of inviscid and viscous flux discretization and temporal derivatives are considered. The advantages of the proposed approach include: the ability to operate on both structured and unstructured meshes; usage of high-order finite difference schemes in time and space; selection of median control volume for discretization of governing equations; application of expressions for calculation of the gradient and pseudo-laplasian making it possible to obtain more accurate results on highly stretched meshes in the boundary layer; writing of equations for the calculation of fluxes through the faces of interior and boundary control volumes in the same form, that simplify software implementation. This approach gives the possibility to implement a strategy of mesh adaptation taking into account the features of the certain flow and gives wide opportunities to parallelize computations. Possibilities of the developed approach are demonstrated on the example of the problem solution related to simulation of unsteady flows in the gas turbine engines.

Keywords: fluid dynamics, unstructured mesh, finite-difference scheme, aerofoil

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