Multivariable DWN Formulation

This section reviews the DWN paradigm and briefly outlines considerations arising in acoustic simulation applications. The multivariable formulation is based on $m$-dimensional vectors of ``pressure'' and ``velocity'' ${\mbox{\boldmath$p$}}$ and ${\mbox{\boldmath$u$}}$, respectively. These variables can be associated with physical quantities such as acoustic pressure and velocity, respectively, or they can be anything analogous such as electrical voltage and current, or mechanical force and velocity. We call these dual variables Kirchhoff variables to distinguish them from wave variables [22] which are their traveling-wave components. In other words, in a 1D waveguide, two components traveling in opposite directions must be summed to produce a physical variable. For concreteness, we will focus on generalized pressure and velocity waves in a lossless, linear, acoustic tube. In acoustic tubes, velocity waves are in units of volume velocity (particle velocity times cross-sectional area of the tube) [27].