The equal width (EW) equation for long waves propagating in the positive x-direction, has the form 0    xxt x t u uu u   (6.1.1) where  and  are positive constants, which require the boundary conditions 0  u as   x .The EW equation is a model nonlinear partial differential equation for the simulation of one-dimensional wave propagation in nonlinear media with dispersion process. Soli...

The present article investigates the thermoelastic interaction in a three-dimensional homogeneous and isotropic sandwich structure using the dual-phase-lag (DPL) model of generalized thermoelasticity. The incorporated resulting non-dimensional coupled equations are applied to a specific problem in which a sandwich layer of unidentical homogeneous and isotropic substances is subjected to time-de...

We present a theoretical study on the tunability of phononic band gaps in two-dimensional phononic crystals consisting of various anisotropic cylinders in an isotropic host. A two-dimensional plane-wave expansion method was used to analyze the band diagrams of the phononic crystals; the anisotropic materials used in this work include cubic, hexagonal, trigonal, and tetragonal crystal systems. B...

Within an acoustic standing wave particles experience acoustic radiation forces, a phenomenon which is exploited in particle or cell manipulation devices. When developing such devices, one-dimensional acoustic characteristics corresponding to the transducer(s) are typically of most importance and determine the primary radiation forces acting on the particles. However, radiation forces have also...

This paper presents an overview of the acoustic wave equation and the common time-domain numerical solution strategies in closed environments. First, the wave equation is presented and its qualities analyzed. Common principles of numerical approximation of derivatives are then reviewed. Based on them, the finite difference (FD) and the finite element methods (FEM) for the solution of the wave e...

Modeling of wave propagation in a heterogeneous medium requires input data that varies on many different spatial and temporal scales. Operator-based upscaling allows us to capture the effect of the fine scales on a coarser domain without solving the full fine-scale problem. The method applied to the constant density, variable sound velocity acoustic wave equation consists of two stages. First, ...

In this work, some strategies and methods, based on finite-difference schemes, are introduced to model the propagation of acoustic waves in a three-dimensional fluid-solid configuration. Specifically, we have considered a heterogeneous propagation medium placed inside a 3D rectangular volume. A plane interface separates the volume into two regions: the first region is a fluid and the second one...

[1] It is shown that the low frequency plasma wave equation can be obtained much more directly than by the previously used method of solving for the determinant of a matrix involving the three components of the electric field vector. The more direct method uses a two-dimensional current density vector space that is precisely equivalent to the previously used three-dimensional electric field vec...

Wave-based methods are increasingly viewed as necessary alternatives to geometric methods for room acoustics simulations, as they naturally capture wave phenomena like diffraction and interference. For methods that simulate the three-dimensional wave equation—and thus solve for the entire acoustic field in an enclosed space—computational costs can be high, so efficient algorithms are critical. ...