Mathematical modelling of the 3D incompressible fluid flows

For the direct numerical simulation of the 3D viscous incompressible fluid flows the Splitting on physical factors Method for Incompressible Fluid flows (SMIF-MERANGE) with hybrid explicit finite difference scheme (second-order accuracy in space, minimum scheme viscosity and dispersion, monotonous) has been used. The applications of the method SMIF-MERANGE for the simulation of the 3D external and internal flows of the viscous incompressible fluid are demonstrated. The detailed formation mechanisms of vortex loops in the sphere wake for the different homogeneous fluid flow regimes are discussed (in the wide range of Reynolds numbers $270<\mathrm{Re}<10^6$). Some examples of the stratified fluid flows around a sphere are considered (for the following ranges of the internal Froude and Reynolds numbers: $0.005<\mathrm{Fr}<1$, $50<\mathrm{Re}<1000$). Some example of the simulation of the air flows in a clean room (CR) is demonstrated.