等几何法在雷诺方程中的应用

The Application of Isogeometric Method in Reynolds Equation

针对有限元法和有限差分法求解雷诺方程精度和效率不高等问题,采用等几何法对雷诺方程进行了求解。建立了雷诺方程的等几何计算模型,给出了等几何求解流程和方法,在MATLAB中开发了等几何计算程序。数值算例求解得出油膜压力图以及不同阶次下压力积分相对误差图,分析了不同自由度和基函数阶次对求解结果的影响。结果表明:采用等几何法求解,大幅减少了表达油膜压力所需的自由度,求解精度和效率相对于有限元法显著提升,同时验证了求解过程中算法的稳定性和求解结果的正确性。

For the problem that solving Reynolds equation with the finite element method and finite difference method is of low accuracy and efficiency, the isogeometric method was used to solve the Reynolds equation. The isogeometric calculation model of Reynolds equation was established, the solving process and method were given, and the calculation procedure was developed in MATLAB.The numerical example gave the oil film pressure diagram and relative error diagrams of pressure integration under different degrees, analyzed the influence of different degrees of freedom and degrees of basis function on the solving results. The result showed that the using of isogeometric method significantly reduced the required degree of freedom to express the oil film pressure;the accuracy and efficiency, compared with the finite element method, significantly improved;at the same time, the stability of algorithm and correctness of the solving results were verified in the solving process.