The Theory and Applications of the SMIF Method for Correct Mathematical Modeling of the Incompressible Fluid Flows
For solving of the Navier-Stokes equations describing the incompressible viscous fluid flows the Splitting on physical factors Method for Incompressible Fluid flows (SMIF) with hybrid explicit finite difference scheme (second-order accuracy in space, minimum scheme viscosity and dispersion, capable for work in the wide range of Reynolds (Re) and internal Froude (Fr) numbers and monotonous) based on the Modified Central Difference Scheme (MCDS) and the Modified Upwind Difference Scheme (MUDS) with a special switch condition depending on the velocity sign and the signs of the first and second differences of the transferred functions has been developed and successfully applied. At the present paper the description of the numerical method SMIF and its applications for simulation of the 3D separated homogeneous and density stratified fluid flows around a sphere and a circular cylinder are demonstrated.
KeywordsDirect numerical simulation Viscous fluid Visualization of the vortex structures Flow regime Sphere Cylinder
This work has been partly supported by Russian Foundation for Basic Research (grants No. \(13-01-92696, 14-01-00428\)), by the programs of the Presidium of RAS No. 15, 18 and by the program No. 3 of the Department of Mathematical Sciences of RAS.
- 10.Matyushin, P.V., Gushchin, V.A.: Direct numerical simulation of the 3D separated viscous fluid flows around the horizontally moving blunt bodies.In: ECCOMAS 2012, e-Book Full Papers, pp. 5232–5241 (2012)Google Scholar
- 11.Gushchin, V.A., Matyushin, P.V.: Mathematical modeling of the 3D separated viscous fluid flows. AIP Conf. Proc. 1487, 22–29 (2012)Google Scholar
- 13.Gushchin, V.A., Narayanan, P.S., Chafle, G.: Parallel computing of industrial aerodynamics problems: clean rooms. In:Schiano, P., Ecer, A., Periaux, J., Satofuka, N. (eds.) Parallel CFD 1997, ELSEVIER Science B.V. (1997)Google Scholar