Integral-Equation Method for Burgers Equation with Geometrical-Spreading Effects
| Autor: | Nobumasa Sugimoto, Kazufumi Ikeda |
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| Rok vydání: | 1997 |
| Předmět: | |
| Zdroj: | Journal of the Physical Society of Japan. 66:2589-2600 |
| ISSN: | 1347-4073 0031-9015 |
| DOI: | 10.1143/jpsj.66.2589 |
| Popis: | This paper presents a new integral-equation method to solve Burgers equation for nonlinear acoustic waves in a duct spreading geometrically along its axis. The nonlinear integral equation is derived by effecting the Cole-Hopf transformation to the Burgers equation and then by applying the Green's function to the equation thus transformed. Under a step initial condition, two methods are demonstrated to solve the integral equation, one being the method of perturbation expansion and the other the method of successive approximation. They are exemplified by solving evolution of an acoustic shock wave in a duct whose cross-sectional area changes abruptly in the form of a step function. It turns out that the method of perturbation expansion gives rise to the non-uniformity to fail in describing a long-time and far-field behavior. By contrast, the method of successive approximation solves the linearized integral equations by iterations infinite times to derive exact solutions if the convergence is attained. It is... |
| Databáze: | OpenAIRE |
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