等几何多重网格法在雷诺方程中的应用

The Application of Isogeometric Multiple Grid Method in Reynolds Equation

相比于有限元法,等几何法求解偏微分方程能以较少的自由度达到更高的求解精度。而多重网格法在处理大规模方程组求解方面应用广泛。为了满足流体仿真对雷诺方程求解的精度与速度的要求,对将等几何法与多重网格法相结合的方法求解雷诺方程进行了研究。文章首先对雷诺方程进行推导,建立适于等几何法的求解模型;然后研究了节点插入的细分算法,构建基于h细化的各层控制点网格之间与阶次相适应的映射矩阵,提出了基于h细化的等几何多重网格法求解模型并。通过不同计算实例发现:等几何多重网格法计算效率明显优于单纯等几何法。

The Isogeometric method(IGA)for PDE equations can achieve higher accuracy with the same freedoms in contrast to the FEM.And the Multi-Grid method(MG)is widely applied in solving large scale equations owing to its high efficiency.In order to expedite the efficiency of solving Reynolds equation through IGA with higher precision requirements,the method of combining IGA and MG was researched.The Reynolds equation was derived at first,then the analysis model suitable for IGA was established;besides,the subdivision algorithm of knot insertion was also studied for developing the Isogeometric multigrid method based on H refinement is and a method of generation reflecting matrix based on H refinement was proposed.Results from different calculation examples showed that:the efficiency of the Isogeometric multigrid method is much better than that of the simple geometric method.