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A fictitious domain method, in which the Dirichlet boundary conditions are treated using boundary supported Lagrangian multipliers, is considered. The technique of the immersed boundary method is incorporated into the framework of the fictitious domain method. Contrary to conventional methods, it does not make use of the finite element discretization. It has a simpler structure and is easily programmable. The numerical simulation of two-dimensional incompressible inviscid uniform flows over a circular cylinder validates the methodology and the numerical procedure. The numerical simulation of propagation phenomena for time harmonic electromagnetic waves by methods combining controllability and fictitious domain techniques is also presented. Using distributed Lagrangian multipliers, the propagation of the wave can be simulated on an obstacle free computational region with regular finite element meshes essentially independent of the geometry of the obstacle and by a controllability formulation which leads to algorithms with good convergence properties for time-periodic solutions. The numerical results presented are in good agreement with those in the literature using obstacle fitted meshes.

We discuss the phenomenology of massless scalar fields around a regular Bardeen black hole, namely absorption cross-section, scattering cross-section and quasinormal modes. We compare the Bardeen and Reissner–Nordström black holes, showing limiting cases for which their properties are similar.

Inflow/Outflow conditions are formulated for time-harmonic waves in a duct governed by the Euler equations. These conditions are used to compute the propagation of acoustic and vortical disturbances and the scattering of vortical waves into acoustic waves by an annular cascade. The outflow condition is expressed in terms of the pressure, thus avoiding the velocity discontinuity across any vortex sheets. The numerical solutions are compared with the analytical solutions for acoustic and vortical wave propagation with and without the presence of vortex sheets. Grid resolution studies are also carried out to discern the truncation error of the numerical scheme from the error associated with numerical reflections at the boundary. It is observed that even with the use of exponentially accurate boundary conditions, the dispersive characteristics of the numerical scheme may result in small reflections from the boundary that slow convergence. Finally, the three-dimensional interaction of a wake with a flat plate cascade is computed and the aerodynamic and aeroacoustic results are compared with those of lifting surface methods.

Discrete methods of numerical analysis have been used successfully for decades for the solution of problems involving wave diffraction, etc. However, these methods, including the finite element and boundary element methods, can require a prohibitively large number of elements as the wavelength becomes progressively shorter. In this work, a new type of interpolation for the acoustic field is described in which the usual conventional shape functions are modified by the inclusion of a set of plane waves propagating in multiple directions. Including such a plane wave basis in a boundary element formulation has been found in the current work to be highly successful. Results are shown for a variety of classical scattering problems, and also for scattering from nonconvex obstacles. Notable results include a conclusion that, using this new formulation, only approximately 2.5 degrees of freedom per wavelength are required. Compared with the 8 to 10 degrees of freedom normally required for conventional boundary (and finite) elements, this shows the marked improvement in storage requirement. Moreover, the new formulation is shown to be extremely accurate. It is estimated that for 2D Helmholtz problems, and for a given computational resource, the frequency range allowed by this method is extended by a factor of three over conventional direct collocation Boundary Element Method. Recent successful developments of the current method for plane elastodynamics problems are also briefly outlined.

A boundary element method (BEM) is presented to study 3D wave scattering by cracks in a cylinder. Green's functions needed in the kernel of boundary integral equations in BEM are derived with the help of guided wave functions. Guided wave modes in the cylinder are obtained by a semi-analytical finite element (SAFE) method. Green's functions are constructed numerically by superposition of guided wave modes. In this method, the cylinder is discretized in the radial direction into several coaxial circular cylinders (sub-cylinders) and the radial dependence of the displacement in each sub-cylinder is approximated by quadratic interpolation polynomials. A numerical procedure is used here to accurately calculate the Cauchy's principal value (CPV) and weakly singular integrals. The multi-domain technique is employed here to model the crack surface. Numerical results are presented to show the effectiveness of the proposed solution.

An analytical model has been developed that can predict the scattering of irregular waves normally incident upon an array of vertical cylinders. To examine the predictability of the developed model, laboratory experiments have been made for the reflection and transmission of irregular waves from arrays of circular cylinders with various diameters and gap widths. Though the overall agreement between measurement and calculation is fairly good, the model tends to over- and under-predict the reflection and transmission coefficients, respectively, as the gap width decreases. The model also underestimates the energy loss coefficients for small gap widths because it neglects the evanescent waves near the cylinders. The peaks of the measured spectra of the reflected and transmitted waves slightly shift towards higher frequencies compared with that of the incident wave spectrum probably because of the generation of shorter period waves due to the interference of the cylinders. Both model and experimental data show that the wave reflection and transmission become larger and smaller, respectively, as the wave steepness increases, which is a desirable feature of the cylinder breakwaters.

An assumption of collinear straight coastlines in the far field, traditionally used in wave models for harbors, is a limitation to wave simulations in the domain extending to infinity, since this assumption is invalid for most real coastlines. By alleviating this limitation based on the geometric-optics approximation, functions of these coastal wave-deformation models are extended to be able to predict wave patterns around the semi-infinite breakwater and convex and concave coasts, such as bulkheads with discontinuous alignment. Mapped infinite elements are also formulated for exterior wave problems. A basic concept in developing is that the true decaying property of scattered waves, i.e. with the modes of r^-1/2, r^-3/2,…, where r is the radial distance, must be represented directly in infinite elements. To do so, a complementary element is introduced to the infinite element. Infinite element integrals can be expressed explicitly because of analytical integrability due to weak singularity in the infinite mapping. Three test problems for coastal wave-deformation models are solved combined with the cubic infinite element with r^-1/2 and r^-3/2 decays; this combination technique is found to be effective and accurate for problems of wave scattering.

In this paper, the combined refraction-diffraction of plane monochromatic waves by a circular cylinder mounted on a conical shoal in an otherwise open sea of constant depth is solved analytically based on the mild-slope equation. At first, Hunt's approximate direct solution for the wave dispersion equation [Hunt, 1979] is used to transform the mild-slope equation with implicit coefficients into an equation with all coefficients being explicitly expressed. This equation is then solved analytically in terms of combined Fourier series and Taylor series. Comparisons are made between the present method and the analytical solutions based on the linear shallow-water equation [Zhu and Zhang, 1996] and the Helmholtz equation [MacCamy and Fuchs, 1954] for long waves and short waves, respectively, and excellent agreements are obtained. For waves in intermediate water depth, comparisons are made with numerical results based on the mild-slope equation and an equally good quality of agreement is achieved. By varying the shoal size, it is found that the wave amplification normally enhances with the increase of shoal, due to the increased contribution from wave refraction. For relatively short wave, the trapped waves by refraction in front of the island interact with the reflected waves and form the partial-standing waves there.

A semi-analytic model is presented for oblique wave scattering by a bottom-standing or surface-piercing flexible porous barrier in water of finite depth with a step-type bottom topography. The physical problem is solved using the methods of least-squares and multi-mode approximation associated with the modified mild-slope equation. Effects on the wave scattering due to bed profile, structural rigidity, compressive force, angle of incidence, barrier length, porosity, and height of the step are examined. The study reveals that under some special conditions, nearly zero/full reflection may occur in the case of wave scattering by a partial flexible porous barrier in the presence of an undulated bottom topography. Further, the study predicts that the Bragg resonance may not occur in the case of wave scattering by a topography of sinusoidal profile. The present study provides insights to help understand how waves are transformed in a marine environment with/without flexible porous barriers in the presence of a bottom topography. The concept and methodology can be generalized to analyze problems of similar nature arising in ocean engineering.

Both lithologic and topographic irregularities may trigger significant scattering phenomenon of seismic waves. In this study, a series solution is presented for the analysis of scattering of SH waves induced by a trapezoidal valley during earthquakes. An appropriate region matching technique is utilized to divide the physical region into four computational subregions. The wave motions of each subregion are obtained as an infinite series of wave functions with unknown coefficients in the respective cylindrical coordinates through wave function expansion method. The Graf's addition theorem is applied to transform the wave potentials of each subregion into the global coordinate. The mixed boundary conditions are solved by truncating the obtained infinite equations into a finite set. The effects of geometrical topographies and sedimentary properties on the amplification are analyzed and discussed in terms of steady-state and transient response analysis.

One of the important factors in the amplification of seismic waves arriving the ground surface is site effects. Site effects, known as topographic irregularities, lead to seismic wave scattering, and this phenomenon can amplify or reduce the displacement recorded in different parts of a site. Therefore, it is necessary to investigate these effects for an accurate evaluation of the dynamic response of the structures built on these sites. One of the topics that has been given little attention is the interaction effects of topographic irregularities on each other’s dynamic responses. Using the three-dimensional boundary element method (3D-BEM) in the frequency domain, this study investigated the dynamic response of the site with canyons and hills adjacent to each other at different intervals and under SH seismic waves with different angles and dimensionless frequencies and with the hill in different geometries (semi-elliptical, triangular, semi-circular). The obtained results indicated that parts of the canyon that are adjacent to the hill underwent the greatest amplification, especially when the distance between the canyon and the hill is small. It was also found that the incident angle of the waves is one of the important parameters in the obtained displacement pattern on the site. Although the wave hit the canyon-hill site vertically, the results revealed that an asymmetric displacement pattern was experienced on the dynamic response of the site due to the phenomenon of amplification of seismic wave dispersion.