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| A numerical method of nonlinear integral equation with singularity |
| Revised:May 28, 2000 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20022036 |
| KeyWord:singular integral equation,numerical method,particle motion |
| Huang Shehua 1 Li Wei 1 Wei Qingding 2 |
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| Abstract: |
| The mathematical properties of a kind of nonlinear integral equation with singularity and corresponding existing condition of solution at particle Reynolds number Rep <1 are studied. Then, a numerical method called P(EC) k multi step difference scheme is developed, its convergence and algebraic accuracy is analyzed and a result of constraint of discrete step in the time domain is obtained. The numerical scheme is applied to calculate a spherical particle's free fall under gravity in quiet fluid and the particle's unsteady motion in oscillating uniform flow field. Compared with analytical solution and experimental result, the method provided in the paper has good accuracy and validity. |
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