Partial acoustic filtering applied to the equations of compressible flow.

摘要

Gas contained in a rectangular enclosure of large length and small width is subjected to large, transient, spatially nonuniform, volumetric heating. The heating timescale 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 are derived from the two-dimensional equations of mass, momentum, and energy conservation for a perfect gas without viscosity or thermal conductivity. This is accomplished 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. The pressure is partitioned into the average pressure across the width, which is O(1), and the small remaining perturbation that is the difference between the pressure and its average. The resulting equations are hyperbolic for the average pressure term but are elliptic for the perturbation pressure term. If an explicit numerical method is used to solve the approximate system, the maximum allowable time step is potentially much larger than the time step for the original system, which is dominated by resolution of pressure waves propagating across the width. Application of partial acoustic filtering to three-dimensional geometries is discussed. 5 refs.