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Acoustodynamics

The IWAVE acoustic package is based on the pressure-velocity form of acoustodynamics, consisting of two coupled first-order partial differential equations:

$\displaystyle \rho \frac{\partial {\bf v}}{\partial t}$	$\textstyle =$	$\displaystyle - \nabla p$	(1)
$\displaystyle \frac{1}{\kappa}\frac{\partial p}{\partial t}$	$\textstyle =$	$\displaystyle -\nabla \cdot {\bf v}+ g$	(2)

In these equations, $p({\bf x},t)$ is the pressure (excess, relative to an ambient equilibrium pressure), ${\bf v}({\bf x},t)$ is the particle velocity, $\rho({\bf x})$ and $\kappa({\bf x})$ are the density and particle velocity respectively. Bold-faced symbols denote vectors; the above formulation applies in 1, 2, or 3D.

The inhomogeneous term represents externally supplied energy (a ``source''), via a defect in the acoustic constitutive relation. A typical example is the isotropic point source

$\begin{displaymath} g({\bf x},t) = w(t) \delta({\bf x}-{\bf x}_s) \end{displaymath}$

at source location ${\bf x}_s$ .

The bulk modulus and buoyancy (reciprocal density) are the natural parameters in a time-stepping discretization of this equation. I will display velocity and density instead. IWAVE's acoustic application converts velocity and density to bulk modulus and buoyancy as part of the problem setup phase.

Next: The dome model - Up: IWAVE Demonstration Package - Previous: Introduction

2012-06-07