A Scale-Selective Multilevel Method for Long-Wave Linear Acoustics

作者：Vater Stefan^*; Klein Rupert; Knio Omar M

来源：Acta Geophysica, 2011, 59(6): 1076-1108.

DOI：10.2478/s11600-011-0037-x

• linear acoustics
• implicit time discretization
• large time steps
• balanced modes
• multiscale time integration

A new method for the numerical integration of the equations for one-dimensional 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. Scale-wise 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.

• 出版日期2011-12