A comparative study on the numerical solution algorithms of gas Reynolds equation

The improved P* algorithm is studied for solving the Reynolds equation by finite difference method. P* algorithm has the advantages of distinct mathematical concepts and simple programming. Firstly, The P* algorithm is combined with the Successive Over-Relaxation (SOR) method, considering the influence of the selection of relaxation factor on the calculation results. The optimal relaxation factor is determined to be 0.97, in this case, the minimum film thickness of flexible gas foil bearing can be calculated to 3.8 μm. Then, by changing the position of P*, the algorithm accuracy, sensitivity to the initial value, and computational efficiency of different P* algorithms are compared and studied. In the end, the P* algorithm is compared with the Newton-Raphson algorithm, it is found that although the Newton-Simpson algorithm computations the matrix dimension is large; but it has the advantages of fast computing speed and high efficiency.