An Efficient Numerical Algorithm For Incompressible Fluid Flow And Heat Transfer Problems With Unstructured Grids

With the continuous development of the computer technology,the computational fluid dynamics and computational heat transfer,the technology to solve these fluid flow and heat transfer problems with complex geometry and strong nonlinearity has become necessary and common.In view of this,it has draw morn attention to develop a computational method,which has the advantage of high prediction precision,strong flexibility,good calculation staility and high efficiency.All these subjects,including the discretization schemes for convection and diffusive terms based on arbitrary grids,the segreaged solving algorithms based on pressure-correction,and the treatment of common boundary conditions,have been studied and improved.The main tasks would be carried out in this paper include:(1)When we deal with the convection term in arbitrary skewed unstructured grids,the principle that the flux on the face depends principally on the variable transported normal to this face should be taken into accout,accordingly,a midperpendicular is constructed to implement the TVD schemes.Based on Gauss' s divergence theorem,two typical interpolation methods for obtaining the facial variable(the G1 method and the G2 method)have been adopted to take into account the difference of variable values between cell centroid and their auxiliary point.The computational experiment indicates that both of these two methods can reduce the error dramatically.With comparing to the G1 method,the G2 method has a higher precision and a better monotony.(2)When we deal with the r-factor algorithm in arbitrary non-uniform unstructured grids,the revised procedure to determine the position of the further upwind node based on the physical meaning of the r-factor is adopted.Furthermore,a fully linear cell averaging procedure is used to evaluate the variable's value of the further upwind node,also when faced with the grid cells near by boundary regions,the procedure to determinate the location and evaluate the variable's value of the further upwind node is would be modified.The computational experiment indicates that with the revised procedure to determine the position and evaluate the variable value of the further upwind node,a higher precision and a better monotony result can be obtained in the framework of nonuniform unstructured grid.(3)This paper proposed a solution procedure to deal with nonlinear fluid flow,which is based on the aforementioned discretized schemes for convection term and diffusion term in the framework of arbitrary unstructured grid.The computational experiment shows that the discretized schemes can obtaine a high precision numerical solution even with skew grids,indicate it has a strong ability of adaptation to grid systems.(4)This paper reviews the solution procedure of the SIMPLE-family algorithm,then the improved algorithm-SIMPLERR algorithm has been proposed based on overcoming the two approximation.The SIMPLERR algorithm introduces an inner iterative process for solving the pressure equation,an inner iterative process includes the pseudo-momentum update,the pressure equation derivative and solution and the velocity explicit correction.The pressure field obtained by the inner iterative process is quite close to its final results of this current outter iterative level,then the consistency issue between the initial pressure and the initial velocity can be overcomed.Hereafter,the pressure correction equation is introduced after solving the implicite discretization momentum equation,the pressure correction term is only used to correct the velocity.Then the pressure field is updated by solving the latest pressure equation,the update process can avoid excessive correction for pressure field,then the second approximation can be overcomed.(5)This paper introduces a revised momentum interpolation method(MIM)in the framework of collocated unstructured grid system,then the SIMPLERR algorithm suit to arbitrary unstructured grid is derived.Thereafter,comprehensive comparisons among the SIMPLER algorithm,the IDEAL algorithm and SIMPLERR algorithm are made for four typical benchmark problems of incompressible fluid flow and heat transfer,the computational experiments indicate that the SIMPLERR algorithm has a stronger robustness and a higher efficience,whether for low-Re/Ra,coarse-mesh flow cases or for high-Re/Ra,fine-mesh flow cases.