Partial Acoustic Filtering Applied to the Equations of Compressible Flow

Abstract

Gas contained in a rectangular laser cell of large length and small width is subjected to large, transient, spatially nonuniform, volumetric heating when pumped. The heating time scale is much longer than the time required for an acoustic wave to traverse the width but can be comparable to the time required for an acoustic wave to traverse the length. Approximate equations describing the motion are derived by applying partial acoustic filtering to the equations of motion: pressure waves traversing the width are removed while pressure waves traversing the length are retained. For a simplified one-dimensional example, a significant density variation is found across the width of the laser cell; moreover, this density variation is in good agreement with a numerical solution of the unapproximated gas dynamic equations although the latter requires two orders of magnitude more computational time