Reflection from the free surface of an inhomogeneous media

1970 ◽  
Vol 60 (4) ◽  
pp. 1101-1104
Author(s):  
H. K. Acharya
Keyword(s):  
Free Surface ◽  
Reflection Coefficient ◽  
Phase Change ◽  
Inhomogeneous Medium ◽  
Shear Wave ◽  
Wave Equations ◽  
Inhomogeneous Media ◽  
Compressional Waves ◽  
Homogeneous Media

abstract A study of the reflection of compressional waves for an elastic, isotropic, inhomogeneous medium in which compressional and shear-wave equations are separable, reveals that, if the properties of the medium are varying slowly, then for real incidence the reflection coefficient for the free surface is complex and the phase change upon vertical reflection is not 180° as is the case for a homogeneous media.

scholarly journals Green’s Function Method for Electromagnetic and Acoustic Fields in Arbitrarily Inhomogeneous Media

2020 ◽  
Author(s):  
Vladimir P. Dzyuba ◽  
Roman Romashko
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Inhomogeneous Medium ◽  
Acoustic Field ◽  
Particle Velocity ◽  
Velocity Vector ◽  
Function Method ◽  
Wave Equations ◽  
Inhomogeneous Media ◽  
Electric Vector

An analytical method based on the Green\'s function for describing the electromagnetic field, scalar-vector and phase characteristics of the acoustic field in a stationary isotropic and arbitrarily inhomogeneous medium is proposed. The method uses, in the case of an electromagnetic field, the wave equation proposed by the author for the electric vector of the electromagnetic field, which is valid for dielectric and magnetic inhomogeneous media with conductivity. In the case of an acoustic field, the author uses the wave equation proposed by the author for the particle velocity vector and the well-known equation for acoustic pressure in an inhomogeneous stationary medium. The approach used allows one to reduce the problem of solving differential wave equations in an arbitrarily inhomogeneous medium to the problem of taking an integral.

scholarly journals Fractional wave equations with attenuation

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Peter Straka ◽  
Mark Meerschaert ◽  
Robert McGough ◽  
Yuzhen Zhou
Keyword(s):  
Wave Equation ◽  
Power Law ◽  
Weak Solutions ◽  
Wave Equations ◽  
Inhomogeneous Media ◽  
Medical Ultrasound ◽  
Sound Waves ◽  
Fractional Wave Equations

AbstractFractional wave equations with attenuation have been proposed by Caputo [5], Szabo [28], Chen and Holm [7], and Kelly et al. [11]. These equations capture the power-law attenuation with frequency observed in many experimental settings when sound waves travel through inhomogeneous media. In particular, these models are useful for medical ultrasound. This paper develops stochastic solutions and weak solutions to the power law wave equation of Kelly et al. [11].

scholarly journals A New Construction for Scalar Wave Equations in Inhomogeneous Media

1997 ◽  
Vol 7 (9) ◽  
pp. 1071-1096 ◽  
Author(s):  
S. de Toro Arias ◽  
C. Vanneste
Keyword(s):  
Wave Equations ◽  
Inhomogeneous Media ◽  
Scalar Wave ◽  
New Construction

Numerical Solution of Thermal and Fluid Flow With Phase Change by VOF Method

2000 ◽  
Author(s):  
Hidemi Shirakawa ◽  
Yasuyuki Takata ◽  
Takehiro Ito ◽  
Shinobu Satonaka
Keyword(s):  
Fluid Flow ◽  
Free Surface ◽  
Phase Change ◽  
Calculation Result ◽  
Bubble Growth ◽  
Present Method ◽  
Spherical Shape ◽  
Superheated Liquid ◽  
One Dimensional ◽  
Solidification Problem

Abstract Numerical method for thermal and fluid flow with free surface and phase change has been developed. The calculation result of one-dimensional solidification problem agrees with Neumann’s theoretical value. We applied it to a bubble growth in superheated liquid and obtained the result that a bubble grows with spherical shape. The present method can be applicable to various phase change problems.

scholarly journals NUMERICAL MODEL OF BREAKWATER WAVE FLOWS

1988 ◽  
Vol 1 (21) ◽  
pp. 149 ◽  
Author(s):  
Alex C. Thompson
Keyword(s):  
Mathematical Model ◽  
Numerical Model ◽  
Reflection Coefficient ◽  
Water Wave ◽  
Wave Equations ◽  
Seepage Flow ◽  
Experimental Results ◽  
Simplified Model ◽  
Flow Equations ◽  
Shallow Water Wave Equations

A mathematical model of flow on a sloping breakwater face is described and results of calculations compared with some experimental results to show how the model can be calibrated. Flow above the surface of the slope is represented by the shallow water wave equations solved by a finite difference method. Flow within the breakwater is calculated by one of two methods. A solution of the linear seepage flow equations, again using finite differences or a simplified model of inflow can be used. Experimental results for runup and reflection coefficient are from tests performed at HRL Wallingford.

scholarly journals Non-linear wave equations for free surface flow over a bump

2020 ◽  
Vol 62 (2) ◽  
pp. 159-169
Author(s):  
Shino Sakaguchi ◽  
Keisuke Nakayama ◽  
Thuy Thi Thu Vu ◽  
Katsuaki Komai ◽  
Peter Nielsen
Keyword(s):  
Free Surface ◽  
Wave Equations ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Linear Wave ◽  
Non Linear ◽  
Linear Wave Equations

A new solution method for the wave equation in inhomogeneous media

Geophysics ◽  
1985 ◽  
Vol 50 (10) ◽  
pp. 1541-1547 ◽  
Author(s):  
D. M. Pai
Keyword(s):  
Wave Equation ◽  
Matrix Method ◽  
Solution Process ◽  
Inhomogeneous Media ◽  
Mathematical Basis ◽  
Vertical Coordinate ◽  
Mathematical Algorithm ◽  
Matching Layer ◽  
Eigen Value ◽  
Homogeneous Media

A fundamental mathematical algorithm is presented for solving the wave equation in inhomogeneous media. This method completely generalizes the Haskell matrix method, which is the standard method for solving the wave equation in laterally homogeneous media. The Haskell matrix method has been the mathematical basis for many seismic techniques in exploration geophysics. In the method presented the medium is divided into layers and vertically averaged within each layer. The wave equation, within a layer, is then decoupled into an eigenvalue equation of the horizontal coordinate and a wave equation of the vertical coordinate. The eigen‐value equation is solved numerically. The vertical equation is solved analytically, once the eigenvalues are found. The solution throughout the medium is constructed by matching layer solutions at layer interfaces. The solution process of this method is “modular,” in the sense that each layer corresponds to an independent module and all the modules together form the final, total solution. Such a modular solution process has the following advantages. First, in a 2-D problem, for example, each module is a 1-D problem, which is a much simpler problem numerically than the original full 2-D problem. Second, the module solutions can be used repeatedly to form the solution corresponding to different problems. For example, in modeling. only those layers which differ between two models require recalculation. The solution to plane‐wave diffraction by a cylinder is obtained using this method, and it agrees well with the analytical solution.

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