A problem of reflection and transmission of a plane shear wave incident at a corrugated Interface between transversely isotropic inhomogeneous and visco-elastic half-spaces is investigated. Applying appropriate boundary conditions and using Rayleigh’s method of approximation expressions for reflection and transmission coefficients are obtained for the first and second order approximation of the corrugation. Further, closed form formulae of these coefficients are presented for a corrugated Interface of periodic shape (cosine law Interface). Numerical computations for this particular type of corrugated Interface are performed and a number of graphs are plotted to illustrate the effect of different parameters of the both half-spaces on the reflection and transmission coefficients. It is found that these coefficients depend upon the amplitude of corrugation of the boundary, angle of incidence and frequency of the incident wave and are strongly influenced by the anisotropy, inhomogeneity and visco-elasticity of the half-spaces. Some special cases are also derived.

The present investigation is concerned with the reflection and transmission coefficients of plane waves at the Interface of generalized thermoelastic solid half space and heat conducting micropolar fluid half- space. The amplitude ratios of various reflected and transmitted waves with various angle of incidence have been computed numerically and depicted graphically. Micropolarity and thermal relaxation effects are shown on the amplitude ratios for specific model. Some special and particular cases are also deduced from the present investigation.

The present study investigates the mathematical inspection of Stoneley wave propagation through the corrugated irregular common Interface of two dissimilar Magnetoelastic Transversely Isotropic (MTI) half-space media under the impression of hydrostatic stresses. To enumerate the Lorentz's force besmeared in the structure, the generalized Ohm's law and Maxwell's equations were considered. The interior deformations were analytically calculated to obtain the wave frequency equation through the prescribed boundary conditions. To investigate the impacts of irregularity and various a ecting parameters such as magnetic couplings and hydrostatic stresses on the wave propagation, frequency curves formed for the phase velocity of the wave.

The existing theory for wave propagation through a soil layer are not compatible with the real soil layers because in the theory the layers are flat and the sub-layers are parallel, while in real the soil layers are not flat and they may not be parallel. Thus, wave propagations through a corrugated Interface are so important. In this paper, two-dimensional SH-wave propagation through a corrugated Interface between two linear transversely isotropic half-spaces is assessed. In order to do this, Lord Rayleigh's method is accepted to express the non-flat surface by a Fourier series. In this way, the amplitude of the reflected and transmitted waves is analytically determined in terms of the incident SH-wave amplitude. It is shown that except for the regular reflected and refracted waves, some irregular reflected and refracted waves are exist, and the amplitudes of these waves vary in terms of the angle and frequency of incident wave, equation of surface, and the material properties of the domains. The numerical computations for some cases of different amplitude/wave-length ratio of the Interface are done. This work is an extension of Asano's paper (1960) for a more complicated Interface, where more non-zero coefficients are considered in expressing the equation of surface in the form of Fourier series. The analytical results for some simpler case of isotropic domain are collapsed on Asano's results (1960). In addition, the numerical evaluation is in good agreement with Asano's.

In finite-volume-based simulations with free-surface waves, it is usually desired to obtain a sharp Interface between both fluid phases. A widely used approach for Interface-capturing and sharpening is the combination of the volume-of-fluid method with the HRIC scheme. The HRIC scheme contains a user-defined parameter, the angle factor, which influences the magnitude of the Interface-sharpening. The present work demonstrates that the optimum value for the angle factor is case dependent: too small values can cause substantial flow disturbances, such as vorticity production within the wave and the occurrence of parasitic wave components, whereas too large values can cause excessive dissipation of wave energy. The optimum value for the angle factor was found to depend on the wave steepness, the aspect ratio of the grid cells, on the cell size and to a lesser degree on the time step size. Results from an extensive parameter study are presented, which can provide guidance for optimizing the angle factor for flow simulations of free-surface wave propagation. Further, two methods are presented which can be used to determine the optimum value of the angle factor. The magnitude of errors that can occur due to improper choices of the angle factor are discussed and recommendations are given to increase the accuracy of flow simulations with free-surface waves.