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One-dimensional fourth-order boundary value problems (BVPs) play a critical role in engineering applications, particularly in the analysis of beams. Current numerical investigations primarily concentrate on homogeneous boundary conditions. In addition to its high precision advantages, the Hermite finite element method (HFEM) is capable of directly computing both the function value and its derivatives. In this paper, both the cubic and quintic HFEM are employed to address two prevalent non-homogeneous fourth-order BVPs. Furthermore, a priori error estimations are established for both BVPs, demonstrating the optimal error convergence order in H 2 semi-norm and L 2 norm. Finally, a numerical simulation is presented to validate the theoretical results. [ABSTRACT FROM AUTHOR]

Inspired by the airway for phonation, fluid flow in an idealized model within a sudden expansion and contraction channel with a geometrically symmetric structure is investigated, and the nonlinear behaviors of the flow therein are explored via numerical simulations. Numerical simulation results show that, as the Reynolds number (Re = U0H/ν) increases, the numerical solution undergoes a pitchfork bifurcation, an inverse pitchfork bifurcation and a Hopf bifurcation. There are symmetric solutions, asymmetric solutions and oscillatory solutions for flows. When the sudden expansion ratio (Er) = 6.00, aspect ratio (Ar) = 1.78 and Re ≤ Rec1 (≈185), the numerical solution is unique, symmetric and stable. When Rec1 < Re ≤ Rec2 (≈213), two stable asymmetric solutions and one symmetric unstable solution are reached. When Rec2 < Re ≤ Rec3 (≈355), the number of numerical solution returns one, which is stable and symmetric. When Re > Rec3, the numerical solution is oscillatory. With increasing Re, the numerical solution develops from periodic and multiple periodic solutions to chaos. The critical Reynolds numbers (Rec1, Rec2 and Rec3) and the maximum return velocity, at which reflux occurs in the channel, change significantly under conditions with different geometry. In this paper, the variation rules of Rec1, Rec2 and Rec3 are investigated, as well as the maximum return velocity with the sudden expansion ratio Er and the aspect ratio Ar. [ABSTRACT FROM AUTHOR]

Wind flow over complex terrain is strongly influenced by the topographical features of the region, resulting in unpredictable local wind characteristics. This paper employs numerical simulation to study the wind flow at a towering peak extending out of a steep mountainside and the wind-induced effect on onsite landscape platforms. First, the wind flow from seven different directions is explored via 3D numerical simulations, and the wind load distribution on the platforms is highlighted. Second, a 2D numerical simulation is conducted to evaluate the wind speedup effect at the side peak, examining the influence of the side peak height and the mountainside steepness on the wind speedup factor. The numerical simulations presented in this research were validated by replicating a published numerical and experimental study. The results illustrate the amplifying and blocking effects of the surrounding topography, yielding unpredictable and nonuniform wind pressure distribution on the platforms. The presence of the side peak leads to a significant increase in the speedup factor, and the side peak height and the mountainside steepness have a moderate influence on the value of the speedup factor. Additionally, the speedup factor obtained from this study varies significantly, especially near the surface, from the recommendations of several wind load standards. Consequently, the impact of the local terrain and the wind speedup effect must be thoroughly assessed to ensure the structural integrity of structures installed at a similar topography. [ABSTRACT FROM AUTHOR]