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| Numerical integration stability control strategies for wave-like part of the havelock form green function |
| Received:May 17, 2012 Revised:September 30, 2012 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx201305011 |
| KeyWord:translating-pulsating source singularity highly oscillatory function integration method stability |
| Author | Institution |
| 许勇 |
海军工程大学 船舶工程系, 武汉 |
| 董文才 |
海军工程大学 船舶工程系, 武汉 |
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| Abstract: |
| The wave-like part of the Havelock form translating-pulsating source Green function is highly oscillatory and discussed.A method based on variable substitution and local refinement of integral steps technique is introduced to calculate the integration by Xu and Dong[4]) which makes calculation efficiency and accuracy possible.But there are still some difficulties in calculation about this method as follows:firstly,the complex function after variable substitution is still discussed when θ=γ; secondly,the y and z direction partial derivatives of the complex function are infinite when θ=π/2; in addition,false singularities (which found by Xu and Dong[4]) become true singularities when Y=0 (where Y=y-ρ, y and ρ are the abscissas of the field and source point) and the integration method may be failed.In order to improve numerical integration stability about this method,some auxiliary techniques are introduced in present study as follows:(1) a limit formula which can remove the singularity of the complex function when θ=γ is used and can avoid calculation overflow.(2) A truncation method is introduced to remove the infinite singularity of the y and z direction partial derivatives when θ=π/2.(3) A region dividing integral method is performed to deal with the singularities and avoid high oscillation when Y=0.False singularities are also studied and it is interest to find that the false singularities should exist when the field point is in the propagation range of the waves produced by the source. |