Stability of Algorithms for Waves with Large Flows

✍ Scribed by Roberto Lionello; Zoran Mikić; Jon A Linker

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 172 KB
• Volume: 152
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1999.6250

✦ Synopsis

We have identified a numerical instability that appears in algorithms for the linear propagation of waves in the presence of an advective flow. This instability is due to the coupling between the advective and wave terms and cannot be identified if stability conditions are derived separately for these two terms. It can appear in explicit or semi-implicit calculations using upwinded or centered spatial differences. We show that a stable scheme can be obtained by introducing a predictor step for the wave terms. When the semi-implicit treatment of the waves is used, the semi-implicit operator must be applied in the predictor step as well as in the corrector step. We present an improved formulation of the semi-implicit coefficient to take advection into account.