Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1076-1108 |
| Number of pages | 33 |
| Journal | Acta Geophysica |
| Volume | 59 |
| Issue number | 6 |
| DOIs | |
| State | Published - Dec 2011 |
| Externally published | Yes |
Keywords
- balanced modes
- implicit time discretization
- large time steps
- linear acoustics
- multiscale time integration
ASJC Scopus subject areas
- Geophysics