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 influe...

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Published inIOP conference series. Materials Science and Engineering Vol. 1081; no. 1; p. 12037
Main Authors Wang, Yongliang, Wang, Yi, Zheng, Longkai
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.02.2021
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ISSN1757-8981
1757-899X
1757-899X
DOI10.1088/1757-899X/1081/1/012037

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Abstract 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.
AbstractList 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.
Author Wang, Yi
Wang, Yongliang
Zheng, Longkai
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Cites_doi 10.1115/1.3254697
10.1115/1.2197526
10.1115/1.1792697
10.1016/j.neucom.2016.08.019
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StartPage 12037
SubjectTerms Algorithms
Comparative studies
Film thickness
Finite difference method
Foil bearings
Mathematical analysis
Matrix methods
Reynolds equation
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