### ASA 127th Meeting M.I.T. 1994 June 6-10

## 4pPA4. Wave propagation with local conservation laws in discrete
Space-Time.

**Raymond J. Nagem
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*Dept. of Aerosp. and Mech. Eng., Boston Univ., 110 Cummington St., Boston,
MA 02215
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The equations of three-dimensional linear acoustics are formulated using a
complex state vector and a first-order Lagrangian. Local conservation equations
for energy, linear momentum, and angular momentum are derived in a unified and
systematic way from gauge transformations. The first-order Lagrangian
description is shown to lead naturally to a set of discrete space and discrete
time field equations. Gauge transformations are again used to derive local
conservation equations for the discrete field variables. Dispersion relations
for the discrete equations are derived, and are used to analyze the spatial
isotropy of propagating waves on the discrete space-time lattice. The solution
of the discrete initial value problem is discussed, as well as its
implementation on a massively parallel computer.