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Öğe Further application of hybrid solution to another form of Boussinesq equations and comparisons(2007) Erduran K.S.Recently, a new hybrid scheme is introduced for the solution of the Boussinesq equations. In this study, the hybrid scheme is used to solve another form of the Boussinesq equations. The hybrid solution is composed of finite-volume and finite difference method. The finite-volume method is applied to conservative part of the governing equations, whereas the higher order Boussinesq terms are discretized using the finite-difference scheme. Fourth-order accuracy is provided in both time and space. The solution is then applied to several test cases, which are taken from the previous studies. The results of this study are compared with experimental and theoretical results as well as those of the previous ones. The comparisons indicate that the Boussinesq equations solved here and in the previous study produce quite similar results. Copyright © 2006 John Wiley & Sons, Ltd.Öğe Hybrid finite-volume finite-difference scheme for the solution of Boussinesq equations(2005) Erduran K.S.; Ilic S.; Kutija V.A hybrid scheme composed of finite-volume and finite-difference methods is introduced for the solution of the Boussinesq equations. While the finite-volume method with a Riemann solver is applied to the conservative part of the equations, the higher-order Boussinesq terms are discretized using the finite-difference scheme. Fourth-order accuracy in space for the finite-volume solution is achieved using the MUSCL-TVD scheme. Within this, four limiters have been tested, of which van-Leer limiter is found to be the most suitable. The Adams-Basforth third-order predictor and Adams-Moulton fourth-order corrector methods are used to obtain fourth-order accuracy in time. A recently introduced surface gradient technique is employed for the treatment of the bottom slope. A new model 'HYWAVE', based on this hybrid solution, has been applied to a number of wave propagation examples, most of which are taken from previous studies. Examples include sinusoidal waves and bi-chromatic wave propagation in deep water, sinusoidal wave propagation in shallow water and sinusoidal wave propagation from deep to shallow water demonstrating the linear shoaling properties of the model. Finally, sinusoidal wave propagation over a bar is simulated. The results are in good agreement with the theoretical expectations and published experimental results. Copyright © 2005 John Wiley & Sons, Ltd.Öğe Theoretical and numerical investigations on solitary wave solutions of Gardner equation(Springer Verlag, 2018) Ak T.; Triki H.; Dhawan S.; Erduran K.S.This paper formulates new hyperbolic functions ansatze to construct exact solitary wave solutions of the Gardner (combined KdV-mKdV) equation and a finite element approach for the numerical solutions. A novel class of exact solitary wave solutions is derived. The conditions on the physical parameters for the existence of the obtained structures are also presented. Accuracy of the proposed numerical scheme is assessed in terms of L2 and L? error norms. Numerical experiments demonstrate the accuracy and robustness of the method which can be further used for solving other nonlinear problems. © 2018, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.
