Basic DWN Formulation

This section reviews the DWN paradigm and briefly outlines considerations arising in acoustic simulation applications.

The formulation is based on dual $m$-dimensional vectors of ``pressure'' and ``velocity'' ${\mbox{\boldmath$p$}}$ and ${\mbox{\boldmath$u$}}$, respectively. These variables can be associated with acoustic pressure and particle- or volume-velocity, or they can be anything analogous such as electrical voltage and current, mechanical force and velocity, etc. We call these dual variables Kirchhoff variables to distinguish them from wave variables which are their traveling-wave components. For concreteness, we will focus on pressure and velocity waves in a lossless, linear, acoustic tube. In acoustic tubes, velocity waves are in units of volume velocity (particle velocity times the tube cross-sectional area) [60].