WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7150
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Article Citation - WoS: 4Citation - Scopus: 4A New Numerical Algorithm Based on Quintic B-Spline and Adaptive Time Integrator for Cou- Pled Burger's Equation(Tabriz University, 2023) Çiçek, Yeşim; Tanoğlu, Gamze; Gücüyenen Kaymak, Nurcan; Bahar, Ersin; Gürarslan, Gürhan; Tanoğlu, Gamze; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyIn this article, the coupled Burger's equation which is one of the known systems of the nonlinear parabolic partial differential equations is studied. The method presented here is based on a combination of the quintic B-spline and a high order time integration scheme known as adaptive Runge-Kutta method. First of all, the application of the new algorithm on the coupled Burger's equation is presented. Then, the convergence of the algorithm is studied in a theorem. Finally, to test the efficiency of the new method, coupled Burger's equations in literature are studied. We observed that the presented method has better accuracy and efficiency compared to the other methods in the literature. © 2023 University of Tabriz. All Rights Reserved.Article A Reliable and Fast Mesh-Free Solver for the Telegraph Equation(Springer, 2022) İmamoğlu Karabaş, Neslişah; Korkut, Sıla Övgü; Tanoğlu, Gamze; İmamoğlu Karabaş, Neslişah; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyIn the presented study, the hyperbolic telegraph equation is taken as the focus point. To solve such an equation, an accurate, reliable, and efficient method has been proposed. The developed method is mainly based on the combination of a kind of mesh-free method and an adaptive method. Multiquadric radial basis function mesh-free method is considered on spatial domain and the adaptive fifth-order Runge–Kutta method is used on time domain. The validity and the performance of the proposed method have been checked on several test problems. The approximate solutions are compared with the exact solution, it is shown that the proposed method has more preferable to the other methods in the literature.Annotation Citation - WoS: 1Citation - Scopus: 1Reply To Comment on “evaluation of a Physically Based Quasi-Linear and a Conceptually Based Nonlinear Muskingum Methods” by Reza Barati(Elsevier Ltd., 2017) Perumal, Muthiah; Tayfur, Gökmen; Rao, C. Madhusudana; Gürarslan, Gürhan; 03.03. Department of Civil Engineering; 03. Faculty of Engineering; 01. Izmir Institute of TechnologyThe writers thank the discusser for his interest in the study of Perumal et al. (2017) and welcome the opportunity to address the issues raised by the discusser. The discusser has mainly raised four issues on the comparative study carried out by Perumal et al. (2017) in evaluating the performances of the VPMM model and the NLM based models, which was initiated by Gill (1977, 1978). These four issues are addressed by these writers in the following pages: As a first issue, the discusser has raised a question about the appropriateness of using the VPMM model (Perumal and Price, 2013), which he considers as the much improved routing model of the Muskingum-Cunge family approach, and the original nonlinear Muskingum model of Gill (1978), which he, perhaps, considers as a initial version of the NLM models. These writers perceive that the discusser intends to convey that the performance evaluation study presented by Perumal et al. (2017) based on a latest improved model and a initial version of the NLM models is inappropriate. Before discussing straightaway on this issue, the writer would like to clarify on the misconception of the discusser in categorizing the VPMM method and the Muskingum-Cunge method under one family approach.Article Citation - WoS: 23Citation - Scopus: 29Evaluation of a Physically Based Quasi-Linear and a Conceptually Based Nonlinear Muskingum Methods(Elsevier Ltd., 2017) Perumal, Muthiah; Tayfur, Gökmen; Rao, C. Madhusudana; Gürarslan, Gürhan; 03.03. Department of Civil Engineering; 03. Faculty of Engineering; 01. Izmir Institute of TechnologyTwo variants of the Muskingum flood routing method formulated for accounting nonlinearity of the channel routing process are investigated in this study. These variant methods are: (1) The three-parameter conceptual Nonlinear Muskingum (NLM) method advocated by Gillin 1978, and (2) The Variable Parameter McCarthy-Muskingum (VPMM) method recently proposed by Perumal and Price in 2013. The VPMM method does not require rigorous calibration and validation procedures as required in the case of NLM method due to established relationships of its parameters with flow and channel characteristics based on hydrodynamic principles. The parameters of the conceptual nonlinear storage equation used in the NLM method were calibrated using the Artificial Intelligence Application (AIA) techniques, such as the Genetic Algorithm (GA), the Differential Evolution (DE), the Particle Swarm Optimization (PSO) and the Harmony Search (HS). The calibration was carried out on a given set of hypothetical flood events obtained by routing a given inflow hydrograph in a set of 40 km length prismatic channel reaches using the Saint-Venant (SV) equations. The validation of the calibrated NLM method was investigated using a different set of hypothetical flood hydrographs obtained in the same set of channel reaches used for calibration studies. Both the sets of solutions obtained in the calibration and validation cases using the NLM method were compared with the corresponding solutions of the VPMM method based on some pertinent evaluation measures. The results of the study reveal that the physically based VPMM method is capable of accounting for nonlinear characteristics of flood wave movement better than the conceptually based NLM method which requires the use of tedious calibration and validation procedures.