A practical guide to multidimensional wave digital algorithms using an example of fluid dynamics
✍ Scribed by Georg Hetmanczyk; Karlheinz Ochs
- Publisher
- John Wiley and Sons
- Year
- 2011
- Tongue
- English
- Weight
- 542 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0894-3370
- DOI
- 10.1002/jnm.768
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✦ Synopsis
Abstract
The wave digital concept for numerical integration of partial differential equations leads to algorithms with highly advantageous features as robustness, full localness and massive parallelism. However, the required synthesis of an internally multidimensionally passive reference circuit, from which the algorithm is derived, usually demands an in‐depth knowledge of circuit theory and a high level of intuition. In this practical guide, a step‐by‐step approach for the synthesis of such reference circuits is introduced to relax these requirements, using the nonlinear fluid dynamic equations as a nontrivial example. General implementation issues for the wave digital algorithm are discussed as well as applying arbitrary passive linear multistep methods in place of the commonly used trapezoidal rule. As an example, we take the well‐known numerically critical shock tube problem, the solution of which is problematic when the trapezoidal rule is used as unwanted oscillations occur. These oscillations are suppressed when using the second‐order accurate Gear method instead. Copyright © 2010 John Wiley & Sons, Ltd.