نوع مقاله : پژوهشی
نویسندگان
1 دانشگاه نوشیروانی بابل
2 هیات علمی/ دانشگاه صنعتی نوشیروانی بابل
چکیده
کلیدواژهها
موضوعات
عنوان مقاله [English]
نویسندگان [English]
The present study proposes a novel approach for solving one-dimensional pure convection problems, utilizing a high-order Taylor Galerkin element-free method. The standard Galerkin method has limitations in solving such problems due to the predominance of convective terms over diffusion terms, leading to unstable and fluctuating analysis results over time. To address this issue, high-order stabilizing terms can be added to the standard Galerkin method. However, due to the limitations in the derivability of the standard Galerkin shape function, it is not possible to incorporate high-order terms in the equation. In this context, the proposed high-order Taylor Galerkin element-free method enables the inclusion of stabilizing terms with high-order derivatives in the equations, utilizing the moving least-squares (MLS) shape function and exponential weight function, which exhibit the continuity of all their derivatives. This approach provides a promising solution for addressing the limitations of the finite element method and achieving more accurate and stable analysis results for one-dimensional pure convection problems. The accuracy of the numerical simulation was evaluated using two one-dimensional pure convection benchmark problems: the Gaussian wave motion problem and the classical water hammer problem, both analyzed up to the fourth-order. The results of the numerical simulations demonstrated that increasing the number of stabilizing terms led to improved accuracy and decreased fluctuations. Therefore, it can be concluded that the stability terms up to the fourth-order in the equations display acceptable accuracy for these two problems. This development has significant implications for the analysis of fluid mechanics and other related phenomena. By enabling a more comprehensive analysis of fluid dynamics, researchers can investigate complex fluid dynamics with greater precision and detail, yielding valuable insights into a wide range of physical processes. In conclusion, the proposed high-order Taylor Galerkin element-free method is a noteworthy advancement in numerical analysis, overcoming the limitations of the standard Galerkin method and demonstrating superior accuracy and stability in the solution of pure convection problems. This approach provides an efficient and accurate method for numerical analysis and has the potential to be extended to other areas of research, including computational fluid dynamics, heat transfer, and structural mechanics.
کلیدواژهها [English]
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