In this work, we investigate wave propagation through a zero index metamaterial (ZIM) waveguide embedded with triangular dielectric defects. We provide a theoretical guidance on how to achieve total reflection and total transmission (i.e., cloaking) by adjusting the defect sizes and/or permittivities of the defects. Our work provides a systematical way in manipulating wave propagation through ZIM in addition to the widely studied dielectric defects with cylindrical and rectangular geometries.

In this paper, the Chebyshev-Galerkin spectral approximations are employed to investigate Poisson equations and the fourth order equations in one dimension. Meanwhile, $p$-version finite element methods with Chebyshev polynomials are utilized to solve Poisson equations. The efficient and reliable a posteriori error estimators are given for different models. Furthermore, the a priori error estimators are derived independently. Some numerical experiments are performed to verify the theoretical analysis for the a posteriori error indicators and a priori error estimations.

The stability behavior of the Leipholz's type of laminated box columns with nonsymmetric lay-ups resting on elastic foundation is investigated using the finite element method. Based on the kinematic assumptions consistent with the Vlasov beam theory, a formal engineering approach of the mechanics of the laminated box columns with symmetric and nonsymmetric lay-ups is presented. The extended Hamilton's principle is employed to obtain the elastic stiffness and mass matrices, the Rayleigh damping and elastic foundation matrices, the geometric stiffness matrix due to distributed axial force, and the load correction stiffness matrix accounting for the uniformly distributed nonconservative forces. The evaluation procedures for the critical values of divergence and flutter loads with/without internal and external damping effects are briefly presented. Numerical examples are carried out to validate the present theory with respect to the previously published results. Especially, the influences of the fiber angle change and damping on the divergence and flutter loads of the laminated box columns are parametrically investigated.

A high-order numerical method for three-dimensional hydrodynamics is presented. The present method applies high-order compact schemes in space and a Runge-Kutta scheme in time to solve the Reynolds-averaged Navier-Stokes equations with the $k-ϵ$ turbulence model in an orthogonal curvilinear coordinate system. In addition, a two-dimensional equation is derived from the depth-averaged momentum equations to predict the water level. The proposed method is first validated by its application to simulate flow in a $180^◦$ curved laboratory flume. It is found that the simulated results agree with measurements and are better than those from SIMPLEC algorithm. Then the method is applied to study three-dimensional hydrodynamics in a natural river, and the simulated results are in accordance with measurements.

In this paper, we consider a singularly perturbed convection-diffusion problem. The problem involves two small parameters that gives rise to two boundary layers at two endpoints of the domain. For this problem, a non-monotone finite element methods is used. A priori error bound in the maximum norm is obtained. Based on the a priori error bound, we show that there exists Bakhvalov-type mesh that gives optimal error bound of $\mathcal{O}(N^{−2})$ which is robust with respect to the two perturbation parameters. Numerical results are given that confirm the theoretical result.

Intrigued by our recent experimental work (H. Yamaguchi and X. D. Niu, J. Fluids Eng., 133 (2011), 041302), the present study numerically investigate the flow-structure interactions (FSI) of three rigid circular particles aligned moving in an inclined channel flow at intermediate Reynolds numbers by using a momentum-exchanged immersed boundary-lattice Boltzmann method. A "frog-leap" phenomenon observed in the experiment is successfully captured by the present simulation and flow characteristics and underlying FSI mechanisms of it are explored by examining the effects of the channel inclined angles and Reynolds numbers. It is found that the asymmetric difference of the vorticity distributions on the particle surface is the main cause of the "frog-leap" when particle moves in the boundary layer near the lower channel boundary.

An computationally efficient damage identification technique for the planar and space truss structures is presented based on the force method and the micro genetic algorithm. For this purpose, the general equilibrium equations and the kinematic relations in which the reaction forces and the displacements at nodes are take into account, respectively, are formulated. The compatibility equations in terms of forces are explicitly presented using the singular value decomposition (SVD) technique. Then governing equations with unknown reaction forces and initial elongations are derived. Next, the micro genetic algorithm (MGA) is used to properly identify the site and extent of multiple damage cases in truss structures. In order to verify the accuracy and the superiority of the proposed damage detection technique, the numerical solutions are presented for the planar and space truss models. The numerical results indicate that the combination of the force method and the MGA can provide a reliable tool to accurately and efficiently identify the multiple damages of the truss structures.

The Ellipsoidal Statistical model (ES-model) and the Shakhov model (S-model) were constructed to correct the Prandtl number of the original BGK model through the modification of stress and heat flux. With the introduction of a new parameter to combine the ES-model and S-model, a generalized kinetic model can be developed. This new model can give the correct Navier-Stokes equations in the continuum flow regime. Through the adjustment of the new parameter, it provides abundant dynamic effect beyond the ES-model and S-model. Changing the free parameter, the physical performance of the new model has been tested numerically. The unified gas kinetic scheme (UGKS) is employed for the study of the new model. In transition flow regime, many physical problems, i.e., the shock structure and micro-flows, have been studied using the generalized model. With a careful choice of the free parameter, good results can be achieved for most test cases. Due to the property of the Boltzmann collision integral, the new parameter in the generalized kinetic model cannot be fully determined. It depends on the specific problem. Generally speaking, the S-model predicts more accurate numerical solutions in most test cases presented in this paper than the ES-model, while ES-model performs better in the cases where the flow is mostly driven by temperature gradient, such as a channel flow with large boundary temperature variation at high Knudsen number.