In this paper, the 2D cracked phononic crystals of in-plane elastic waves are studied based on the local radial basis function collocation method (LRBFCM). The direct method is used to solve the instability caused by the derivative calculation of the LRBFCM in the crack. The band structure of the cracked phononic crystals according to the wave vectors in the first Brillouin Zone is presented. The relationship between the band structure and the cracks with different lengths and positions is fully studied. Different acoustic impedance ratios, filling rates, and lattice forms are considered. The numerical results are validated by the band structures obtained from the FEM, which also show interesting phenomenon of the cracked phononic crystals.
The evaporation of liquid lens widely occurs in various scientific and industrial applications. In this study, a theoretical model is set up for liquid lens evaporation under the axisymmetric toroidal coordinate, with coupled internal heat conduction and external vapor diffusion. The effect of evaporative cooling number, liquid lens shape and volume on evaporation performance is quantitatively analyzed. It is found that overall evaporation rate is determined by the competing effect of evaporation flux and area of upper surface. With the increasing ratios of upper and lower tangential angles, at high evaporative cooling numbers or large liquid volumes, overall evaporation rates decrease firstly, after reaching the minimum value, they start to increase until the asymptotic value. The "2/3 power law" holds for transient volume variation of liquid lens over time, independent of evaporative cooling and liquid lens shape. These findings may help get insight into the liquid lens evaporation on immiscible liquid.
Based on the notion that the numerical technique should consider and examine the conservation and convergence of the inherent properties for the original system, we construct and analyze a structure-preserving algorithm for the Klein-Gordon-Schrödinger equation using the averaged vector field Galerkin spectral element method in this paper. First, we discretize the fundamental equation in spatial direction via the spectral element method based on the weak form of the system, which yields a Hamiltonian ordinary differential equation. Second, the averaged vector field method is used to solve the resulted Hamiltonian system to obtain an energy-preserving and numerically charge-preserving scheme for the Klein-Gordon-Schrödinger equation. The higher-order fully-discrete schemes in time direction are also obtained by applying the corresponding higher-order averaged vector field method. Then, the error estimate is given with the convergence order of $\mathcal{O}(∆t^2 + ∆x^{min(N,r)}N^{−r})$ in the discrete $L^2$-norm, where $N$ is the order of the cardinal basis functions, $r$ represents the order of the Sobolev space, $∆t$ and $∆x$ are time and space steps, respectively. Finally, numerical experiments are conducted to verify the theoretical analysis well.
A numerical study was conducted on the flow induced vibration of an eight-spined cactus-shaped cylinder under subcritical Reynolds numbers. The influence of porous spines with different Darcy numbers $(Da=10^{–4}$ to $10^{–2})$ and different arrangements (W1, W2, L1, L2) on the vibration control performance of the cactus cylinder was investigated. The results indicate that the arrangement significantly impacts the control effectiveness. The cactus cylinder configuration W1, featuring five porous spines arranged on the windward side and a Darcy number of $10^{–2},$ effectively suppressed VIV, achieving reductions of 73.1% in amplitude, 31.3% in mean drag, and 84.8% in root mean square lift. However, improper arrangements, such as the L1 configuration with five porous spines arranged on the leeward side, induced galloping in the cylinder structure, leading to further divergence and amplification of the vibration amplitude.
This paper presents the analytical study of inertialess instability in a three-layer film flow on an incline at a low capillary number.Using the Maple software enabled us to expand the advantages of the analytical approach to study the instability growth rate as a function of the middle-layer viscosity and thickness. Assuming that the capillary number at the surface is a small parameter, we obtained the asymptotic approximation of the instability growth rate. The comparative study of three-layer films and channel flows was conducted using the asymptotic approximation in both the symmetrical case and the case of weak thickness asymmetry.Our focus was on the so-called dominant wave number, for which the growth rate of the instability is at a maximum. We derived the approximations of the dominant wave number and the corresponding maximum instability growth rate, as well as their partial derivatives with respect to the middle-layer viscosity and thickness. The basic properties of the dominant wave number and the corresponding maximum growth rate were determined using the zeros and singular points of the partial derivatives. The obtained results were compared with the experimental data.
