Method of Streeter and Wylie for multidimensional wave propagation

Fluid dynamic and wave propagation problems in two or three dimensions are sometimes calculated using the method of Streeter and Wylie. In this method, the fluid sheet or volume is represented by a network or lattice of fluid-filled pipes having finite flow-area, but assumed to intersect at ideal points. The one-dimensional equations are then solved for each pipe (or ''leg''), subject to continuity of pressure and to conservation of mass at each junction (or ''node''). It is explicitly demonstrated that the Streeter-Wylie method, with a first-order-accurate one-dimensional algorithm for the legs, provides a first-order accurate algorithm for the two-dimensional fluid equations in the linear acoustic limit where the particle velocity is much less than the sonic velocity, and where material properties are time-independent. The requirements are that the sonic velocity be scaled, and that the flow area per width in the network be independent of direction. Results for several simple example calculations are presented and compared with known exact results