A boundary integral approach to analyze the viscous scattering of a pressure wave by a rigid body

The paper provides boundary integral equations for solving the problem of viscous scattering of a pressure wave by a rigid body. By using this mathematical tool uniqueness and existence theorems are proved. Since the boundary conditions are written in terms of velocities, vector boundary integral equations are obtained for solving the problem. The paper introduces single-layer viscous potentials and also a stress tensor. Correspondingly, a viscous double-layer potential is defined. The properties of all these potentials are investigated.By representing the scattered field as a combination of a single-layer viscous potential and a double-layer viscous potential the problem is reduced to the solution of a singular vectorial integral equation of Fredholm type of the second kind.In the case where the stress vector on the boundary is the main quantity of interest the corresponding boundary singular integral equation is proved to have a unique solution.     

Numerical analysis of the inviscid incompressible flow in two-dimensional radial-flow pump impellers

The flow through a two-dimensional centrifugal impeller fitted with equiangular blades of arbitrary geometry is investigated using a combination of conformal mapping with a boundary element technique. The blades can be thin or thick of arbitrary cross-section. A theoretical analysis and a numerical procedure are developed to determine the pressure distributions along the blade.     

Analytic determination of the capacitance matrix of planar orcylindrical multiconductor lines on multilayered substrates

An exact analytical expression for the Maxwell capacitance matrix of a multilayer, multistrip planar or cylindrical line is derived by solving the dual series equation system of the problem by means of a Volterra boundary-value problem. The solution is expressed in terms of some infinite matrices with very good convergence properties. Numerical examples show that the method yields accurate results and is also computationally effective for lines having a large number of conductors     

Determination of the macrodispersive parameters of a motion in a two-layer porous medium

Summary This paper develops a method for deriving good estimates of macrodispersive transport parameters describing the asymptotic evolution of a non-reactive chemical pollutant injected into a two-layer porous medium. These parameters are extracted from the coefficients of asymptotic time-polynomial expansions of some adequately chosen integral transforms performed upon the solution of the original transport problem.     

Analytically determined quasi-static parameters of shielded or openmulticonductor microstrip lines

An exact analytical expression for the capacitance matrix of a shielded or open multiconductor microstrip structure is derived by solving the system's dual integral equations by constructing a Volterra boundary-value problem (BVP). The solution is expressed in terms of infinite matrices with very good convergence properties. This new approach uses a series of Bessel functions rather than trigonometric series to approximate the solution which results in an efficient algorithm. Simplified formulas are given for the even and odd capacitance of symmetric coupled microstrip lines and compared to the results given by the finite analytical solution available in this particular case. Numerical examples demonstrate that the method yields accurate results and is computationally effective for structures having a large number of conductors     

The scattering of a scalar wave by a thin oblate body of revolution

The scattering of a scalar incident wave by a thin oblate body of revolution is studied. The scattering wave is represented as a distribution of ring singularities in a disk inside the body. Boundary conditions result in one-dimensional integral equations for singularity distributions. The asymptotic solution of these equations for thin bodies furnishes the singularity distribution as well as the radius α of the disk containing ring singularities. Example of the plane wave axially incident upon an oblate ellipsoid is presented. The total scattering cross-section is computed.     

Potential due to some arbitrarily charged strips between parallel earthed planes

The potential problem in the infinite region $\text{D = {(x, y)¦?∞ < x < ∞, 0 < y < c}}$ is considered for the case of the mixed Dirichlet-Neumann boundary conditions. The problem is formulated as a Volterra modified problem for a complex function and the solution of this last problem is written explicitly. In the case of the constant boundary data (i.e. constant potentials of the strips) the solution has been written in a simpler form.     

A microacoustic analysis including viscosity and thermal conductivity to model the effect of the protective cap on the acoustic response of a MEMS microphone

An analysis is presented of the effect of the protective cover on the acoustic response of a miniature silicon microphone. The microphone diaphragm is contained within a small rectangular enclosure and the sound enters through a small hole in the enclosure’s top surface. A numerical model is presented to predict the variation in the sound field with position within the enclosure. An objective of this study is to determine up to which frequency the pressure distribution remains sufficiently uniform so that a pressure calibration can be made in free space. The secondary motivation for this effort is to facilitate microphone design by providing a means of predicting how the placement of the microphone diaphragm in the package affects the sensitivity and frequency response. While the size of the package is typically small relative to the wavelength of the sounds of interest, because the dimensions of the package are on the order of the thickness of the viscous boundary layer, viscosity can significantly affect the distribution of sound pressure around the diaphragm. In addition to the need to consider viscous effects, it is shown here that one must also carefully account for thermal conductivity to properly represent energy dissipation at the system’s primary acoustic resonance frequency. The sound field is calculated using a solution of the linearized system consisting of continuity equation, Navier–Stokes equations, the state equation and the energy equation using a finite element approach. The predicted spatial variation of both the amplitude and phase of the sound pressure is shown over the range of audible frequencies. Excellent agreement is shown between the predicted and measured effects of the package on the microphone’s sensitivity.