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The experiment results show that the optimal laser pulse energy of precision control in laser shock semi-die forming is 15 J; and forming error can be reduced by more than 50% with the method of contours modification and compensation.
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The numerical section exposes the method of contour dynamics, designed specifically for applications in which conservation of vorticity is important.
In this paper we consider the time evolution of vortices simulated by the method of contour dynamics.
Alternatively (and this is a remark I got from Martin Klaus) one can evaluate the right side, I, of (A.11) by the method of contour integrals.
Sound generation due to the interaction between two inviscid coaxial vortex rings moving along a common axis in the same direction is investigated numerically by using the method of contour dynamics and the far field equations.
The method of contour dynamics, developed for two-dimensional vortex patches by Zabusky et al. [N.J. Zabusky, M.H. Hughes, K.V. Roberts, Contour dynamics for the Euler equations in two-dimensions, J. Comp. Phys. 30 (1979) 96 106] is extended to vortex rings in which the vorticity distribution varies linearly with normal distance from the symmetry axis.
A simplified approach in which the method of constant deflection contour lines [1] is used is presented in this paper to analyze the large amplitude free vibrations of thin elastic plates.
At present, other effective methods for solving inverse spectral problems have been created; among them we point out the method of spectral mappings connected with ideas of the contour integration method.
The method of spectral mappings is connected with the idea of the contour integration method and reduces the inverse problem to the so-called main equation of the inverse problem, which is a linear equation in the Banach space of bounded sequences.
To overcome these shortcomings, in this paper, we present a method of contour extraction synchronizing with edge tracking but omitting the thresholding process.
The method represents contours of potential vorticity as a spectral sum and solves the Biot-Savart equation for the velocity by spectrally evaluating a desingularized contour integral.
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