利用Ringleb流动对有限体积法精度的研究

Study on Accuracy of Central Finite Volume Methods Using Ringleb Flow

利用有精确解的Ｒｉｎｇｌｅｂ 流动构造了用于检验流场计算精度的工具，并用这种工具对中心有限体积法的精度进行了研究。深入讨论了网格、边界处理、人工粘性等对计算精度的影响。结果定量地证明了改善边界处理的精度、网格的正交性，包括边界正交性和场内正交性，都可以提高流场计算的精度。为了减少人工粘性对无粘流计算的干扰，应该尽量降低人工粘性系数。

There is usually considerable difference between the theoretical accuracy and the actual performance of the existing numerical methods and schemes in CFD (Computational Fluid Dynamics). We use Ringleb flow as a tool to estimate the actual accuracy of numerical methods. First we calculate the flow field inside a Ringleb flow tube with a specific numerical method; then we compare the numerical results with the analytical solution, which is accurate; thus, we can know the error and its distribution of the method. We use this method to study the accuracy of central finite volume methods. Figs.(4) through (10) show the influence of grid quality, boundary treatment and artificial viscosity on its accuracy as follows: (1) Grid with good orthogonality and rational clustering can greatly improve its accuracy (Figs.4 through 8). (2) Careful construction of boundary scheme is also important (Fig.9). (3) The artificial viscosity coefficients should be kept as small as possible in order to suppress the error caused by artificial viscosity to inviscid flow calculation (Fig.10).