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This paper is dealing with numerical simulation of generalized Newtonian and generalized Oldroyd-B fluids with the aim of blood flow simulation. The Newtonian model of a fluid cannot capture all the phenomena in many fluids with complex microstructure, such as polymers, suspensions (also many biological fluids) and granular materials. The motion of polymeric fluids is described by the conservation of mass and momentum. One shall assume that the fluid is incompressible and temperature variations are negligible. When one considers viscoelastic behavior of polymeric fluids, the extra stress tensor depends not only on the current motion of the fluid, but also on the history of the motion. In this case the extra stress tensor is decomposed into its Newtonian part and its elastic part. Components of the elastic part of the extra stress tensor are computed using the Oldroyd-B constitutive equation. Time derivative of the pressure is added into the continuity equation (Artificial compressibility method) and the arising system of equations is discretized in space with Finite volume method and numerically solved in time with Runge-Kutta method. Numerical methods are tested in the geometry of constricted channel. [ABSTRACT FROM AUTHOR]

This study deals with the numerical solution of a 2D unsteady flow of a compressible viscous fluid in a channel for low inlet airflow velocity. The unsteadiness of the flow is caused by a prescribed periodic motion of a part of the channel wall with large amplitudes, nearly closing the channel during oscillations. The flow is described by the system of Navier-Stokes equations for laminar flows. The numerical solution is implemented using the finite volume method (FVM) and the predictor-corrector Mac-Cormack scheme with Jameson artificial viscosity using a grid of quadrilateral cells. Due to the motion of the grid, the basic system of conservation laws is considered in the arbitrary Lagrangian-Eulerian (ALE) form. The numerical results of unsteady flows in the channel are presented for inlet Mach number M8 = 0.012, Reynolds number Re8 = 4481, and the wall motion frequency 100 Hz. [ABSTRACT FROM AUTHOR]

Abstract: This paper is interested in the numerical approximation of the turbulent 3D incompressible flow. The turbulent flow is mathematically modeled using the Reynolds averaged Navier–Stokes (RANS) equations and two classes of the turbulent models are considered. RANS equations are approximated by two numerical techniques, the finite volume and the finite element methods. The finite element approximation on general 3D domains using general meshes consisting of hexahedrons as well as tetrahedrons, pyramids and prisms is described. The definition of the continuous piecewise trilinear/linear finite element space is given, and the stabilization based on the streamline-upwind/Petrov–Galerkin method together with the pressure stabilizing/Petrov–Galerkin techniques is used. The turbulence model is approximated on the finite element spaces, and the nonlinear stabilization technique is applied. Furthermore, the finite volume technique is used for the approximation of the RANS equations. The turbulent or the explicit algebraic Reynolds stress models are used. The numerical solution is carried out by the implicit finite volume method. The artificial compressibility method is used to solve the incompressibility constraint. The numerical results are shown. [Copyright &y& Elsevier]

Highlights: [•] 2D and 3D simulations of backward facing step flows. [•] Step perpendicular or inclined, top wall parallel or inclined. [•] Used finite element and finite volume method. [•] Used eddy viscosity and EARSM turbulence models. [•] All results compared with experimental data. [ABSTRACT FROM AUTHOR]

Abstract: The paper deals with numerical solution of laminar and turbulent flows of Newtonian and non-Newtonian fluids in branched channels with two outlets. Mathematical model of the flow is based on the Reynolds averaged Navier–Stokes equations for the incompressible fluid. In the turbulent case, the closure of the system of equations is achieved by the explicit algebraic Reynolds stress (EARSM) turbulence model. Generalized non-Newtonian fluids are described by the power-law model. The governing equations are solved by cell-centered finite volume schemes with the artificial compressibility method; dual time scheme is applied for unsteady simulations. Channels considered in presented calculations are of constant square or circular cross-sections. Numerical results for laminar flow of non-Newtonian fluid are presented. Further, turbulent flow through channels with perpendicular branch is simulated. Possible methods for setting the flow rate are discussed and numerical results presented for two flow rates in the branch. [Copyright &y& Elsevier]

Abstract: The work deals with the numerical simulation of turbulent flow through turbine cascades including heat exchange between fluid and blades. The numerical algorithm couples an implicit AUSM finite volume solver for fluid flow and a finite element solver for heat conduction inside the blade. Several k-ω turbulence models are applied. The eddy diffusivity assumption is used for turbulent heat flux computation. The influence of inlet boundary conditions for turbulence models is discussed. A case of failure of eddy diffusivity turbulent heat flux with common value of turbulent Prandtl number Pr t =0.91 is presented, where remedy is achieved by lowering the magnitude of Pr t . [Copyright &y& Elsevier]