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A scale-selective multilevel method for long-wave linear acoustics

Vater S., Klein R., Knio O.M.

Acta Geophysica

2011

Vol. 59, no. 6

1076-1108

A new method for the numerical integration of the equations for onedimensional linear acoustics with large time steps is presented. While it is capable of computing the "slaved" dynamics of short-wave solution components induced by slow forcing, it eliminates freely propagating compressible short-wave modes, which are under-resolved in time. Scalewise decomposition of the data based on geometric multigrid ideas enables a scale-dependent blending of time integrators with different principal features. To guide the selection of these integrators, the discrete-dispersion relations of some standard second-order schemes are analyzed, and their response to high wave number low frequency source terms are discussed. The performance of the new method is illustrated on a test case with "multiscale" initial data and a problem with a slowly varying high wave number source term.