Abstract
A new method is presented for the computation of two-dimensional periodic progressive surface waves propagating under the combined influence of gravity and surface tension. The nonlinear surface is expressed by Fourier series with finite number of terms, after the computational domain is transformed into a unit circle. The dynamic boundary equation is used in its exact nonlinear form and the coefficients of Fourier series are found by the Newton-Raphson method successively. This is a neat method, Yielding high prescision with little computational effort.
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Schwartz, L. W., Numerical solution of the exact equations for capillary-gravity waves,J. Fluid Mech.,95, Part 1 (1979), 119–139.
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Communicated by Tsai Shu-tang
Dedicated to the Tenth Anniversary and One Hundred Numbers of AMM (I)
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Qi-su, Z., Yao-song, C. & Bao-yuan, Q. A novel method of solving the exact equations for capillary-gravity waves. Appl Math Mech 12, 309–312 (1991). https://doi.org/10.1007/BF02098061
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DOI: https://doi.org/10.1007/BF02098061