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Abstract <p>The development of the splitting method for incompressible fluid flows (SMIF) during last 45 years is described. The hybrid explicit finite difference scheme of method SMIF is based on modified central difference scheme (MCDS) and modified upwind difference scheme (MUDS) with special switch condition depending on the velocity sign and the signs of the first and second differences of transferred functions. Application of this method for solving of some tasks (the spatial flow around a sphere and a circular cylinder for homogeneous and stratified fluids (in a wide range of dimensionless parameters of the problem, including the transitional regimes (2D–3D transition, laminar-turbulent transition in the boundary layer)); a plane problem of fluid flows with a free surface; a dynamics of vortex pair in a water; a collapse of spots in stratified fluid; the air, heat, and mass transfer in “clean rooms”) is demonstrated.</p>

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Development and Application of the SMIF Method for the Investigation of Incompressible Fluid Flows

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • V. A. Gushchin

摘要

Abstract

The development of the splitting method for incompressible fluid flows (SMIF) during last 45 years is described. The hybrid explicit finite difference scheme of method SMIF is based on modified central difference scheme (MCDS) and modified upwind difference scheme (MUDS) with special switch condition depending on the velocity sign and the signs of the first and second differences of transferred functions. Application of this method for solving of some tasks (the spatial flow around a sphere and a circular cylinder for homogeneous and stratified fluids (in a wide range of dimensionless parameters of the problem, including the transitional regimes (2D–3D transition, laminar-turbulent transition in the boundary layer)); a plane problem of fluid flows with a free surface; a dynamics of vortex pair in a water; a collapse of spots in stratified fluid; the air, heat, and mass transfer in “clean rooms”) is demonstrated.