Laminar incompressible flow past a class of blunted wedges using the Navier-Stokes equations

The Navier-Stokes equations are solved, numerically, to determine the symmetric laminar incompressible flow past blunted wedges. Similarity-type variables are used in a coordinate system that comprises the optimal coordinates for the corresponding boundary-layer problem. This formulation leads to better numerical accuracy and produces the correct solution near the leading edge, far downstream and transversely far from the wedge surface. The flow over parabolas, the flat plate, and the verticval wall are obtained as particular cases of the present solutions and compare well with the available results for these problems. The numerical method that converges rapidly to accurate results.     

The numerical solution of the Navier-Stokes equations for laminar incompressible flow past a paraboloid of revolution

A numerical methods is presented for the solution of the Navier-Stokes equations for flow past a paraboloid of revolution. This method is based upon the ideas of van de Vooren and collaborators [1,2]. The flow field has been computed for a large range of Reynolds numbers. Results are presented for the skinfriction and the pressure together with their respective drag coefficients. The total drag has been checked by means of an application of the momentum theorem.     

Three-dimensional laminar incompressible flow in straight polar ducts

The flow in the entrance region of long ducts of rectangular and polar cross sections is studied using the three-dimensional parabolized Navier-Stokes equations, together with the energy equation, for an incompressible viscous fluid. Numerical solutions are obtained using an alternating-direction implicit technique for the parabolized equations which are elliptic in the cross-plane of the duct, and the calculations march forward in the axial direction. Computations are also made for polar ducts with a rotating outer-radial wall so as to provide meaningful results for a model problem comprising the simplest form of a turbomachinery cascade. The study of this model problem serves to analyze some of the important features of three-dimensional internal viscous flows. Also of interest is the rapidly converging solution of the Neumann problem for the cross-plane variation of pressure for polar ducts.     

Calculating viscous incompressible flow past an elliptical cylinder on a parallel computer

An algorithm developed for a parallel computer is described. The algorithm has been simulated on an ES-1060 machine, and the results are compared with those obtained on BÉSM-6 computer.Translated from Kibernetika, No. 1, pp. 64–68, January–February, 1990.     

Lattice Boltzmann computations of incompressible laminar flow and heat transfer in a constricted channel

A multi-population thermal lattice Boltzmann method (TLBM) is applied to simulate incompressible steady flow and heat transfer in a two-dimensional constricted channel. The method is validated for velocity and temperature profiles by comparing with a finite element method based commercial solver. The results indicate that, at various Reynolds numbers, the average flow resistance increases and the heat transfer rate decreases in a constricted channel in comparison to a straight channel. The effect of the constriction ratio is also investigated. The results show that the presented numerical model is a promising tool in analyzing simultaneous solution of fluid flow and heat transfer phenomena in complex geometries.     

A three-dimensional numerical model for incompressible two-phase flow of a granular bed submitted to a laminar shearing flow

A numerical model for the simulation of incompressible two-phase flows of a flat granular bed submitted to a laminar shearing flow is presented, considering a two-fluid model and a mixed-fluid one. The governing equations are discretized by a finite element method and a penalisation method is introduced to cope with the incompressibility constraint. A regularisation technique is used to deal with the visco-plastic behaviour of the granular phase. Validations are carried out on three flow test cases: a Bingham fluid between two infinite parallel planes, a Bingham fluid in a square lid-driven cavity and a Newtonian fluid over a granular bed in a two-dimensional configuration, for which we compare our numerical results with existing analytical or numerical results. The accuracy and efficiency of the numerical models have been compared for the two formulations of the two-phase flow model. It turns out that the two-fluid model requires ten times more CPU time than the mixed-fluid one for a comparable accuracy, which can be achieved provided one takes a smaller regularisation parameter in the latter model. Finally, three-dimensional computations are presented for the flow of a Newtonian fluid over a granular bed in a square and circular cross-section ducts.     

High-order accurate simulation of low-Mach laminar flow past two side-by-side cylinders using spectral difference method

This paper reports development of a two-dimensional solver for compressible viscous flow using spectral difference (SD) method and its applications on simulating laminar flow past two side-by-side cylinders at various spacings. The high-order spectral difference solver is based on unstructured quadrilateral grids. High-order curved wall boundary representation is developed for cylinders. Nine different spacings (center-to-center distance/diameter s = 1.1, 1.4, 1.5, 1.7, 2, 2.5, 3, 3.4 and 4) are investigated. The simulation results are compared to experimental results and other numerical results. As s increases, single bluff-body, flip-flopping, anti-symmetric and symmetric wake patterns are predicted.     

Time-dependent solutions of the viscous incompressible flow past a circular cylinder by the method of series truncation

Semi-analytic solutions of the Navier-Stokes equations are calculated for two-dimensional, symmetrical, viscous incompressible flow past a circular cylinder. The stream and vorticity functions are expanded in the finite Fourier series and then substituted in the Navier-Stokes equations. This led to a system of coupled parabolic partial differential equations which are solved numerically. More terms of the series are required as Reynolds number increases and the present calculations were terminated at Reynolds number 600 with 60 terms of Fourier series. The results are compared with similar calculations and experimental data for Reynolds numbers 60, 100, 200, 500, 550 and 600. At the termination of the calculations for Reynolds numbers 60 and 100, the separation angle, the wake length, the drag coefficient, and the vorticity distributions around the surface were very close to their steady-state values. A secondary vortex appeared on the surface of the cylinder in the case of Reynolds numbers 500, 550 and 600. The wake length, the drag coefficient and the separation angle differ slightly at a given instant in the case of Reynolds numbers 500, 550 and 600.     

Boundary control of a laminar flow of a viscous incompressible fluid in the generalized Couette cell. The asymptotic approach

In this paper, a limiting problem for an optimal boundary control problem of a laminar flow of a viscous incompressible fluid in the generalized Couette cell, when the number of inner cylinders unrestrictedly increases, is obtained.     

Aspects of unsteady incompressible flow simulations

Since unsteady incompressible flow simulations involving complex geometry require long computing times, it is crucial to select computationally efficient solvers. For this purpose, two numerical procedures, one based on artificial compressibility and the other pressure projection method, are investigated for obtaining time-accurate solutions of the incompressible Navier–Stokes equations. The performance of the two methods is compared by obtaining unsteady solutions for the evolution of twin vortices behind a flat plate. Calculated results are compared with experimental and other numerical results. For an unsteady flow, which requires small physical time step, the pressure projection method was found to be computationally efficient since it does not require a subiteration procedure. It was also observed that the artificial compressibility method requires a fast convergence scheme at each physical time step in order to satisfy the incompressibility condition. This was obtained by employing a GMRES-ILU(0) solver in the artificial compressibility solver.     

Preconditioning strategies for models of incompressible flow

We describe some new preconditioning strategies for handling the algebraic systems of equations that arise from discretization of the incompressible Navier-Stokes equations. We demonstrate how these methods adapt in a straightforward manner to decisions on implicit or explicit time discretization, explore their use on a collection of benchmark problems, and show how they relate to classical techniques such as projection methods and SIMPLE.     

Chebyshev solution of laminar boundary layer flow

An expansion procedure using the Chebyshev polynomials is proposed by using El-Gendi method [1], which yields more accurate results than those computed by P. M. Beckett [2] and A. R. Wadia and F. R. Payne [6] as indicated from solving the Falkner-Skan equation, which uses a boundary value technique. This method is accomplished by starting with Chebyshev approximation for the highest-order derivative and generating approximations to the lower-order derivatives through integration of the highest-order derivative.     

A finite point method for incompressible flow problems

A stabilized finite point method (FPM) for the meshless analysis of incompressible fluid flow problems is presented. The stabilization approach is based in the finite increment calculus (FIC) procedure developed by O?ate [14]. An enhanced fractional step procedure allowing the semi-implicit numerical solution of incompressible fluids using the FPM is described. Examples of application of the stabilized FPM to the solution of two incompressible flow problems are presented. Received: 30 June 1999 / Accepted: 21 September 1999     

A domain decomposition method for almost incompressible flow

A domain decomposition method for solving the Navier-Stokes equations for almost incompressible flow is examined. At the price of a nonuniform decomposition of the domain, we have fast solvers in all subdomains. Hence, each iteration on the Schur complement system can be performed very efficiently. We have shown theoretically that the method requires much fewer memory positions and arithmetic operations than a direct method. Numerical experiments show that the iteration on the Schur complement system converges very fast. We also show that the spatial grid ratio might be crucial for the performance of the method. Moreover, we show that for a given discretization of the problem, the rate of efficiency is larger than 100% for the problem studied here, due to the very nice parallelization properties of the algorithm.     

Solution domain decomposition method for viscous incompressible flow

A solution domain decomposition method is developed for steady state solution of the biharmonic-based Navier-Stokes equations. It consists of a domain decomposition in conjunction with Chebyshev collocation for spatial discretization. The interactions between subdomains are effectively decoupled by means of a superposition of auxiliary solutions to yield a set of independent elementary problems which can be solved concurrently on multiprocessor computers. Assessments are carried out to a number of test problems including the two-dimensional steady flow in a driven square cavity. Illustrative examples indicate a good performance of the proposed methodology which does not affect the convergence and stability of the discretization scheme. Spectral accuracy is retained with absolute error decaying in an exponential fashion. The numerical solutions for the driven cavity compare favorably against previously published numerical results except for a slight overprediction in the vertical velocity component at Reynolds number of 400. TheC ³ continuity is speculated to be its cause.     

不可压缩流两重稳定有限体积算法应用研究

通过将局部高斯积分稳定化方法和两重网格算法思想紧密结合,提出了粘性不可压缩流体的两重稳定有限体积算法。将该算法的三种迭代格式进行了效率的分析比较。理论分析和数值实验发现：当粗、细网格尺度比例选择适当时,两重算法与传统算法具有相同精度解的同时,效率大大提高;对不同格式的两重有限体积算法进行比较分析发现：Simple格式计算效率最高,Picard格式次之,Newton格式较低。     

A fully explicit method for incompressible flow computation

A new formulation of the Navier–Stokes equations is introduced to solve incompressible flow problems. It keeps the benefits of the penalty method, that is, velocity and pressure can be obtained separately and no pressure-Poisson equation is involved. Unlike the penalty method the formulation is more stable or less stiff and then explicit time integration can be applied for easy implementation. No linear or nonlinear system need be solved in the method. In the case that a large number of time steps are needed a parallelization based on domain decomposition is applied to reduce the computational time. With the explicit time integration the parallel implementation and its message passing are very simple as well.     

Pseudospectral multi-domain method for incompressible viscous flow computation

We present a multi-domain pseudospectral method for the calculation of incompressible viscous flow. Governing equations are written in primitive variables formulation. Velocity components and pressure are discretized on the same grid of collocation points. A coupling algorithm for the Stokes problem is investigated and preliminary results are presented in the two-dimensional case.     

Numerical solution of incompressible flow through branched channels

The work deals with numerical solution of 3D turbulent flow in straight channel and branched channels with two outlets. The mathematical model of the flow is based on Reynolds-averaged Navier–Stokes equations for incompressible flow in 3D with explicit algebraic Reynolds stress turbulence model (EARSM). The mathematical model is solved by artificial compressibility method with implicit finite volume discretization. The channels have constant square or circular cross-section, where the hydraulic diameter is same in order to enable comparison between these numerical simulations. First, developed flow in a straight channel of square cross-section is presented in order to show the ability of the used EARSM turbulence model to capture secondary corner vortices, which are not predicted by eddy viscosity models. Next the flow through channels with perpendicular branch is simulated. Methods of setting the flow rate are discussed. The numerical results are presented for two flow rates in the branch.     

Viscous flow past circular cylinders

Accurate and efficient calculation of the flow around a circular cylinder are presented for Reynolds number from 1 to 40 (based on the diameter). The semi-analytical method of series truncation is used to express the stream function and the vorticity in a finite Fourier series. Substitution into the Navier-Stokes equation yields a finite system of nonlinear ordinary differential equations. These are approximated by two-point boundary value methods. The resulting nonlinear equation are solved unsing Newton's method. Much attention has been given to numerical errors and errors resulting from the approximation by a finite series. The results are compared with similar calculations by Keller-Takami and Dennis-Chang. The agreement is good. The application of free stream conditions at a finite radius is shown to yield inaccurate results. im