JAEM 2011, Vol 1, No 1
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Öğe An application of modified reductive perturbation method to symmetric regularized-long-wave(Işık University Press, 2011-03-24) Demiray, HilmiIn this work, we extended the application of "the modified reductive perturbation method" to symmetrical regularized long waves with quadratic nonlinearity and obtained various form of KdV equations as the governing equations. Seeking a localized travelling wave solutions to these evolution equations we determined the scale parameters g(1) and g(2) so as to remove the possible secularities that might occur. To indicate the power and elegance of the present method, we compared our result with the exact travelling wave solution of the symmetric regularized long-wave equation with quadratic nonlinearity. These results show that for weakly nonlinear case the solutions for both approaches coincide with each other. The present method is seen to be fairly simple as compared to the renormalization method of Kodama and Taniuti [4] and the multiple scale expansion method of Kraenkel et al [6].Öğe Computational and asymptotic methods in aeroacoustics with applications(Işık University Press, 2011) Delale, Can Fuat; Zafer, Baha; Aslan, Alim RüstemIn this article the computational and asymptotic methods used in aeroacoustics are reviewed. In particular, two different aeroacoustic applications are demonstrated.In the first problem we investigate the first and second order asymptotic predictions of the thickness and loading noise of a subsonic B-bladed helicopter rotor in the far field and compare the SPL noise results with those of full numerical computations. The results of the second order asymptotic formula seem to be in better agreement with full numerical computations than the first order asymptotic formula. In the second problem, the effect of acoustic wave propagation in transonic nozzle flow is investigated by solving the unsteady quasi-one-dimensional transonic nozzle equations in conservative form using high order computational aeroacoustic schemes, where a novel non-reflecting boundary condition is implemented in addition to the standard non-reflecting boundary condition using characteristics. Excellent agreement with the exact solution is obtained in each case.
