A numerical scheme for the wave simulations of the Kuramoto–Sivashinsky model via quartic-trigonometric tension B-spline


Wave Motion, vol.114, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 114
  • Publication Date: 2022
  • Doi Number: 10.1016/j.wavemoti.2022.103045
  • Journal Name: Wave Motion
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Kuramoto-Sivashinsky model, Shock wave, Chaotic simulations, Turbulent flow, Benchmark problem, COLLOCATION METHOD, LIQUID-FILM, EQUATION, LAMINAR, FLOW
  • Eskisehir Osmangazi University Affiliated: Yes


© 2022 Elsevier B.V.In this work, the numerical investigation of the Kuramoto–Sivashinsky model with the application of the relatively-new proposed tension B-spline function, is studied. The numerically computed scheme is conducted with the hybridizable approach using collocation method in space and time directions. The spatial discretization results in the time-dependent system of equations. Then, the system is integrated by Crank–Nicolson technique which finally generates wholly constructed space–time scheme. Therefore, numerical solution of the Kuramoto–Sivashinsky model is obtained. The stability of the numerical scheme is performed by considering the stability matrix. Then, the stable regions have been presented in terms of the eigenvalues of the linearized system. The efficiency of the computational procedure is confirmed on sample problems. These numerical experiments are also studied to demonstrate the well-known characteristics of the model equation. In particular, dynamics of shock-waves, periodic nature and turbulent flows have been illustrated. The hybrid collocation scheme have successfully generated the nonlinear wave behavior of the Kuramoto–Sivashinsky model.