| Numerical predictions(or numerical simulations) for turbulent flow is the base project in fluid flow and heat transform.He yongsen et al find that fully developed incompressible turbulent flow in a conical diffuser having a total divergence of 8~0 and an area ratio of 4:1 can be simulated by a DLR turbulent model and it's BFC(Boundary-Fitted Coordinates) method,but the predictions for turbulent flow have low efficiency.Algebraic multi-grid methods are by far the most,efficient methods for solving large scale algebraic systems arising from discretizations of PDEs or a system of PDEs.Generally speaking,there are two types of multigrid methods:geometric-based approach and algebraic approach.The large computers have developed very fast and the function of computer have been improved in recent years,which make the multigrid methods vary from optimal algorithm theoretically to optimal algorithm in practice.Since the complexities for practical application problems and the requirements for the "plug and play" solvers in numerical business softwares,it is difficult to construct a sequence of nested discretizations or meshes needed for geometric multigrid method. The algebraic multigrid method(AMG) has become the hotspot due to the high performance and robustness.In this paper,we make some in-depth studies for applying the AMG algorithms in numerical predictions for turbulent flow.A detailed discussion of implement procession of applying AMG methods to simulate the turbulent flow.Focus on improving the efficiency of simulation,we put forward some feasible methods.A number of numerical experiments have been performed.The computational results are compared with the results of experimental results,and some crucial numerical results are obtained.These researches will make the AMG algorithms richer and apply the AMG methods to more researching fields.The main contents and results are listed as followings:1.A convergence criterion is posed in numerical computation and thus the steps of time are made by the mode of self-adaptive control.Compared with experimental results,the numerical results can be accepted.In the picture about the curve of convergent history,the errors of time step n+1 and time step n keep little variation.2.By the precondition of finite difference method,We use the AMG methods in the field of numerical prediction of turbulent flow.A detailed implement process of the AMG method is given in this paper.The process of generating coefficient matrix of different difference schemes is also given in this paper and the method is introduced in detail.The method about how the boundary conditions are embed in the algebraic systems is studied,we develop the joint programs of the AMG method and the program DLRAMG,DHRAMG.Under the same computational condition and control precision,the AMG method is more efficient,than the SOR method which was often used in the past and about one-third of the total CPU time can be saved.3.Focus on the problem that the number of nodes of 13 points difference scheme is much and the computation cost much time,we design a new 5 points difference scheme.This new 5 points scheme has less non-zero elements than the 13 points scheme in the their systems and then the cost time for computation can be dccrcascd.Numerical experiments show that one third of CPU time can be saved.4.In this paper,a new method is posed to gcncratc the BFC gird with the adjustable boundary mesh intervals and orthogonality.The real examples show that the grids can be generated by the method for the simple connected and mutli-connected regions with complicated boundary.5.In addition,in this paper,a body-fitted non-orthogonal collocated grid system is generated. The standardκ-εmodel and the wall function are adopted.Numerical simulation is done for turbulent flow around 2-D single sinusoidal hill and two sinusoidal hills.Non-orthogonal collocated grid-based SIMPLE algorithm is adopted for solving the coupling system of the velocity and pressure equations.Simulation results agree well with the cxperimental data.
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