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Numerical Simulation of Kelvin–Helmholtz Instability Using Split-Step Fourier and Exponential Time-Integrators | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 05 مهر 1405 اصل مقاله (2.56 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.67493.3219 | ||
| نویسنده | ||
| Kolade M Owolabi* | ||
| 1. Department of Mathematical Sciences, Federal University of Technology Akure, PMB 704, Akure, Ondo State, Nigeria. 2. Department of Software Engineering, Faculty of Engineering and Natural Sciences, Fenerbahçe University, Istanbul 34758, Türkiye. 3. Department of Mathematics and Applied Mathematics, School of Science and Technology, Sefako Makgatho Health Sciences University, Ga-Rankuwa 0208, South Africa. | ||
| چکیده | ||
| This paper investigates the application of two high-order numerical methods—the Split-Step Fourier Method (SSFM) and the Exponential Time-Differencing Runge--Kutta 4 (ETDRK4) scheme—in solving complex two-dimensional incompressible Navier--Stokes flows, with emphasis on the Kelvin--Helmholtz instability (KHI). These methods are effective in resolving diverse fluid dynamic phenomena such as shear-layer vorticity, vortex roll-up, and streaming instabilities with high fidelity. The SSFM excels at resolving the stiff viscous terms and preserving spectral accuracy in space, while ETDRK4 is adept at efficiently integrating stiff temporal dynamics present in the Cahn--Hilliard phase field formulations. To justify the suitability and accuracy of these proposed methods, we conduct extensive convergence studies and validate our results against analytical growth rates. Furthermore, we perform a comparative analysis with a higher-order finite difference method (FDM), demonstrating that SSFM and ETDRK4 achieve superior accuracy, stability, and efficiency. Convergence tests reveal exponential spatial accuracy and fourth-order temporal accuracy for the proposed methods, in contrast to the lower-order behavior of FDM. These findings affirm the robustness of SSFM and ETDRK4 in capturing fine-scale structures and long-time evolution of complex hydrodynamic instabilities, making them particularly well-suited for simulating turbulent transitions, multi-vortex dynamics, and flow-interface interactions encountered in geophysical, astrophysical, and engineering applications. | ||
| کلیدواژهها | ||
| Vorticity؛ Hydrodynamic instabilities؛ Numerical simulations | ||
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آمار تعداد مشاهده مقاله: 5 تعداد دریافت فایل اصل مقاله: 2 |
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