Large scale computations in fluid dynamics

Abstract

Many phenomena in the nature may be considered in the frame of the incompressible fluid flows. Such flows are described by the Navier-Stokes equations. As usually we have deal with the flows with large gradients of hydrodynamic parameters (flows with a free surface, stratified fluid flows, separated flows, etc.). For direct numerical simulation of such flows finite difference schemes should possess by the following properties: high order of accuracy, minimum scheme viscosity, dispersion and monotonicity. The Splitting on the physical factors Method for Incompressible Fluid flows (SMIF) with hybrid explicit finite difference scheme 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 has been developed. This method has been successfully applied for the flows with a free surface including regimes with broken surface wave, for 3D separated homogeneous and stratified fluid flows around a sphere and a circular cylinder including transitional regimes. The air, heat and mass transfer in the clean rooms for the pharmaceutical industry is considered. The parallelization of the algorithm has been made and applied on the massive parallel computers with a distributed memory. Some examples of calculated problems will be discussed.