中文摘要：

机械和矿山工程中广泛使用锥形渐扩管。将DLR型k-ε紊流模型中非线性偏微分方程基于全隐式高精度迎风差分格式离散．得到差分方程的系数矩阵为五对角块十三对角带状稀疏矩阵，基于一种“三元组”方式进行压缩存储，节约内存。提出了一种基于DLR型k-ε紊流模型与代数多重网格方法结合的新算法，阐述了代数多重网格方法的实施过程。对具有逆压梯度流动的锥形渐扩管内紊流进行了数值预测。数值实验表明，代数多重网格方法对求解紊流模型离散方程组非常有效，同此前该紊流数值模拟中使用的Point-SOR方法相比，计算效率有了显著提高，计算结果与实验结果吻合较好。

英文摘要：

A conical diffuser has been widely used in mechanical and mine engineering. DLR k-ε turbulent model is discreted by finite difference method. A full implicit difference scheme of high precision based on 13 points node stencil is constructed. Large sparse matrices with 13 diagonals are formed. The sparse matrices are compressively stored by three one-dimension arrays for saving memory. The algebraic multi- grid method is a popular fast algorithm which is used to solve the discrete systems of differential equations. Numerical method of integrating the DLR k-ε turbulent model with the algebraic multigrid method are posed and the detailed implement process is given. Numerical experiments are shown that the computational efficiency is improved and the numerical results agree well with the experiment results.