Sharif Digital Repository

Transmission line formulation is used to analyze two-dimensional low-loss metallic gratings at optical frequencies when plasmonic waves propagate in the structure. This method, like the Fourier modal method, suffers from numerical instabilities when applied to such structures. A systematic approach to avoid these instabilities is presented. These numerical artifacts are attributed to the violation of Li's inverse rule and the appearance of higher-order spurious modes. In this paper, a new approach is proposed to identify and to greatly reduce the effect of these spurious modes based on the accuracy by which these modes are satisfying the conservation of momentum. Furthermore, the proposed... 

Multiphase problems with high density ratios and complex interfaces deal with numerical instabilities and require accurate considerations for capturing the multiphase interfaces. An Incompressible Smoothed Particle Hydrodynamics (ISPH) scheme is presented to simulate such problems. In order to keep the present scheme simple and stable, well-established formulations are used for discretizing the spatial derivatives and a repulsive force is applied at the multiphase interface between particles of different fluids to maintain the interface sharpness. Special considerations are included to overcome the difficulties to model severe physical discontinuities at the interface and surface tension... 

The technique of adaptive spatial resolution is for the first time applied in fast and efficient Fourier-based analysis of metallic lamellar gratings at microwave frequencies. Inasmuch as the ultrahigh-contrast permittivity profile of these structures is likely to incur numerical instabilities, the continuity condition is heedfully imposed on the transverse electromagnetic fields and an elegant, unconditionally stable matrix-based strategy is proposed to rigorously analyze the microwave transmission of these structures. © 2009 IEEE  

A hydroelastic hybrid model is developed to simulate the fluid-structure interaction in water entry problems using the partitioned approach. The interactions between a flat plate and the water are modeled by a hydroelastic model using explicit and implicit couplings. Both couplings are unstable due to numerical instability associated with the fluid added mass. To overcome the instability, an extended Wagner's model is combined with the hydroelastic model, and a hybrid model is developed. The extended Wagner's model is the extension of the classical Wagner's model that is used to estimate the fluid inertial, damping, and restoring forces of a flexible plate within the potential flow theory.... 

A smeared crack approach has been proposed to model the static and dynamic behavior of mass concrete in three-dimensional space. The proposed model simulates the tensile fracture on the mass concrete and contains pre-softening behavior, softening initiation, fracture energy conservation and strain rate effects under dynamic loads. It was found that the proposed model gives excellent results and crack profiles comparing with the available data under static loads. Morrow Point dam was analyzed including dam-reservoir interaction effects to consider its nonlinear seismic behavior. It was found that the resulted crack profiles are in good agreement with the contour of maximum principal stresses... 

A numerical treatment for the prediction of cavitating flows is presented and assessed. The algorithm uses the preconditioned multiphase Euler equations with appropriate mass transfer terms. A central difference finite volume scheme with suitable dissipation terms to account for density jumps across the cavity interface is shown to yield an effective method for solving the multiphase Euler equations. The Euler equations are utilized herein for the cavitation modeling, because some certain characteristics of cavitating flows can be obtained using the solution of this system of equations with relative low computational effort. In addition, the Euler equations are appropriate for the assessment... 

Dynamic deformations of beams and plates under moving objects have extensively been studied in the past. In this work, the dynamic response of geometrically nonlinear rectangular elastic plates subjected to moving mass loading is numerically investigated. A rectangular von Karman plate with various boundary conditions is modeled using specifically developed geometrically nonlinear plate elements. In the available finite element (FE) codes the only way to distinguish between moving masses from moving loads is to model the moving mass as a separate entity. However, these procedures still do not guarantee the inclusion of all inertial effects associated with the moving mass. In a prepared... 

The objective of this work is to numerically study the fluid flow and acoustic field of a supersonic impinging jet by applying the vorticity confinement (VC) method. For this aim, the three-dimensional compressible Navier-Stokes equations with the incorporation of the VC method are considered and the resulting system of equations is solved by using the sixth-order compact finite-difference scheme. To eliminate the numerical instability, a low-pass high-order filter is used. The nonreflective boundary conditions are applied for all the free boundaries and the radiated sound field is obtained by the Kirchhoff surface integration. Comparisons of the present results with the experimental data... 

The objective of this work is to numerically study the fluid flow and acoustic field of a supersonic impinging jet by applying the vorticity confinement (VC) method. For this aim, the three-dimensional compressible Navier-Stokes equations with the incorporation of the VC method are considered and the resulting system of equations is solved by using the sixth-order compact finite-difference scheme. To eliminate the numerical instability, a low-pass high-order filter is used. The nonreflective boundary conditions are applied for all the free boundaries and the radiated sound field is obtained by the Kirchhoff surface integration. Comparisons of the present results with the experimental data... 

Planar grating diffraction analysis based on Legendre expansion of electromagnetic fields is reported. In contrast to conventional RCWA in which the solution is obtained using state variables representation of the coupled wave amplitudes; here, the solution is expanded in terms of Legendre polynomials. This approach, without facing the problem of numerical instability and inevitable round off errors, yields well-behaved algebraic equations for deriving diffraction efficiencies, and can be employed for analysis of different types of gratings. Thanks to the recursive properties of Legendre polynomials, for longitudinally inhomogeneous gratings, wherein differential equations with non-constant... 

It has been recently shown that guided modes in two-dimensional photonic crystal based structures can be fast and efficiently extracted by using the Galerkin's method with Hermite-Gauss basis functions. Although quite efficient and reliable for photonic crystal line defect waveguides, difficulties are likely to arise for more complicated geometries, e.g., for coupled resonator optical waveguides. First, unwanted numerical instability may well occur if a large number of basis functions are retained in the calculation. Second, the method could have a slow convergence rate with respect to the truncation order of the electromagnetic field expansion. Third, spurious solutions are not unlikely to...