NUMERICAL INVESTIGATION OF THREE-DIMENSIONAL VISCOUS INCOMPRESSIBLE FLOWS IN DIVERGENT CURVED CHANNELS AND TURBULENT MODEL STUDY

In order to make the numerical calculation of viscous flows more convenient for the flows in channel with complicated profile governing equations expressed in the arbitrary curvilinear coordinates were derived by means of Favre density-weighted averaged method, and a turbulent model with effect of curvature modification was also derived. The numerical calculation of laminar and turbulent flown in divergent curved channels was carried out by means of parabolizeil computation method. The calculating results were used to analyze and investigate the aerodynamic performance of talor cascades in compressors preliminarily.

On the modeling of viscous incompressible flows with smoothed particle hydrodynamics

Smoothed particle hydrodynamics （SPH） is a Lagrangian, meshfree particle method and has been widely applied to diffe- rent areas in engineering and science. Since its original extension to modeling free surface flows by Monaghan in 1994, SPH has been gradually developed into an attractive approach for modeling viscous incompressible fluid flows. This paper presents an overview on the recent progresses of SPH in modeling viscous incompressible flows in four major aspects which are closely related to the computational accuracy of SPH simulations. The advantages and disadvantages of different SPH particle approximation sche- mes, pressure field solution approaches, solid boundary treatment algorithms and particle adapting algorithms are described and analyzed. Some new perspectives and fuRtre trends in SPH modeling of viscous incompressible flows are discussed.

An analysis of the incompressible viscous flows problem by meshless method

Generally the incompressible viscous flow problem is described by the Navier-Stokes equation. Based on the weighted residual method the discrete formulation of element-free Galerkin is inferred in this paper. By the step-bystep computation in the field of time, and adopting the least-square estimation of the-same-order shift, this paper has calculated both velocity and pressure from the decoupling independent equations. Each time fraction Newton-Raphson iterative method is applied for the velocity and pressure. Finally, this paper puts the method into practice of the shear-drive cavity flow, verifying the validity, high accuracy and stability.

An Immersed Method Based on Cut-Cells for the Simulation of 2D Incompressible Fluid Flows Past Solid Structures

We present a cut-cell method for the simulation of 2D incompressible flows past obstacles.It consists in using the MAC scheme on cartesian grids and imposing Dirchlet boundary conditions for the velocity field on the boundary of solid structures following the Shortley-Weller formulation.In order to ensure local conservation properties,viscous and convecting terms are discretized in a finite volume way.The scheme is second order implicit in time for the linear part,the linear systems are solved by the use of the capacitance matrix method for non-moving obstacles.Numerical results of flows around an impulsively started circular cylinder are presented which confirm the efficiency of the method,for Reynolds numbers 1000 and 3000.An example of flows around a moving rigid body at Reynolds number 800 is also shown,a solver using the PETSc-Library has been prefered in this context to solve the linear systems.

THE FINITE VOLUME PROJECTION METHOD WITH HYBRID UNSTRUCTURED TRIANGULAR COLLOCATED GRIDS FOR INCOMPRESSIBLE FLOWS

In this article a finite volume method is proposed to solve viscous incompressible Navier-Stokes equations in two-dimensional regions with corners and curved boundaries. A hybrid collocated-grid variable arrangement is adopted, in which the velocity and pressure are stored at the centroid and the circumcenters of the triangular control cell, respectively. The cell flux is defined at the mid-point of the cell face. Second-order implicit time integration schemes are used for convection and diffusion terms. The second-order upwind scheme is used for convection fluxes. The present method is validated by results of several viscous flows.

NONLINEAR GALERKIN METHOD AND CRANK-NICOLSONMETHOD FOR VISCOUS INCOMPRESSIBLE FLOW

In this article we discuss a new full discrete scheme for the numerical solution of the Navier-Stokes equations modeling viscous incompressible flow. This scheme consists of nonlinear Galerkin method using mixed finite elements and Crank-Nicolson method. Next, we provide the second-order convergence accuracy of numerical solution corresponding to this scheme. Compared with the usual Galerkin scheme, this scheme can save a large amount of computational time under the same convergence accuracy. (Author abstract) 8 Refs.

The energy transfer mechanism of a perturbed solid-body rotation flow in a rotating pipe

Three-dimensional direct numerical simulations of a solid-body rotation superposed on a uniform axial flow entering a rotating constant-area pipe of finite length are presented. Steady in time profiles of the radial, axial, and circumferential velocities are imposed at the pipe inlet. Convective boundary conditions are imposed at the pipe outlet. The Wang and Rusak (Phys. Fluids 8:1007-1016, 1996.) axisymmetric instability mechanism is retrieved at certain operational conditions in terms of incoming flow swirl levels and the Reynolds number. However, at other operational conditions there exists a dominant, three-dimensional spiral type of instability mode that is consistent with the linear stability theory of Wang et al. (J. Fluid Mech. 797: 284-321, 2016). The growth of this mode leads to a spiral type of flow roll-up that subsequently nonlinearly saturates on a large amplitude rotating spiral wave. The energy transfer mechanism between the bulk of the flow and the perturbations is studied by the Reynolds-Orr equation. The production or loss of the perturbation kinetic energy is combined of three components: the viscous loss, the convective loss at the pipe outlet, and the gain of energy at the outlet through the work done by the pressure perturbation. The energy transfer in the nonlinear stage is shown to be a natural extension of the linear stage with a nonlinear saturated process.

THE IMPLICIT METHOD OF STREAMLINE ITERATION FOR COMPUTING TWO-DIMENSIONAL VISCOUS INCOMPRESSIBLE FLOW

This paper presents the implicit method of streamline iteration on the bases of the method of streamline itera- tion for computing two-dimensional viscous incompressible steady flow in a channel with arbitrary shape. A new total pressure equation of viscous incompressible flow is introduced in this paper and the equation is numerically computed by the implicit method. It is shown from the computational results of examples that the implicit method of streamline iteration can speed up the convergence and decrease the computational time.

An Accurate Cartesian Method for Incompressible Flows with Moving Boundaries

An accurate cartesian method is devised to simulate incompressible viscous flows past an arbitrary moving body.The Navier-Stokes equations are spatially discretized onto a fixed Cartesian mesh.The body is taken into account via the ghost-cell method and the so-called penalty method,resulting in second-order accuracy in velocity.The accuracy and the efficiency of the solver are tested through two-dimensional reference simulations.To show the versatility of this scheme we simulate a threedimensional self propelled jellyfish prototype.

HIGH ACCURATE SOLUTION OF INCOMPRESSIBLE VISCOUS FLOW WITH PRIMATIVE VARIABLE

This paper presents a higher order difference scheme for the computation of the incompressible viscous flows. The discretization of the two-dimensional incompressible viscous Navier-Stokes equations, in generalized curvilinear coordinates and tensor formulation, is based on a non-staggered grid. The momentum equations are integrated in time using the four-stage explicit Runge-Kutta algorithm [1] and discretized in space using the fourth-order accurate compact scheme [2]. The pressure-Poisson equation is discretized using the nine-point compact scheme. In order to satisfy the continuity constraint and ensure the smoothness of pressure field, an optimum procedure to derive a discrete pressure equation is proposed [9][3] . The method is applied to calculate the driven cavity flow on a stretched grid with the Reynolds numbers from 100 to 10000. The numerical results are in very good agreement with the results obtained by Ghia et al [7] and include the periodic solutions for high Reynolds numbers.

ParalelComputationofViscousFluidFlow

A parallel numerical method is employed to solve the two dimensional Navier Stokes equations in primitive variables for incompressible flow.The computing process contains two sections.The first section uses the GE (group explicit) method with high parallelism to solve the velocity equations.The second section solves the pressure equation by a successive underrelaxtion iteration method in red black order.Results are given using these methods on a parallel computer.Until recently,GE method has rarely been used to solve the Navier Stokes equations.

OPERATOR SPLITTING SCHEMES FOR THE NON-STATIONARY THERMAL CONVECTION PROBLEMS

In this work, a new numerical scheme is proposed for thermal/isothermal incompressible viscous flows based on operator splitting. Unique solvability and stability analysis are presented. Some numerical result are given, which show that the proposed scheme is highly efficient for the thermal/isothermal incompressible viscous flows.