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Appendix B: Applications in Fluid Dynamics

In Appendix B, we summarize some of the interesting new developments in applying wave digital filtering methods to strongly nonlinear problems in fluid dynamics. Though there are no significant new results in this appendix, we take the opportunity to elucidate some connections to current trends in the analysis of such systems involving so-called skew self-adjoint forms; in doing so, we highlight certain unforeseen shortcomings of Fettweis's MDKC and MDWD network representations of these systems, and indicate a possible way of avoiding these difficulties in §B.3.3 by making use of entropy variables. In keeping with the overall goal of unifying wave digital and digital waveguide network approaches to numerical integration, we also show in §B.3.2 how the methods of §4.10 can be applied to the one-dimensional gas dynamics system in order to yield a DWN-like structure.

Stefan Bilbao 2002-01-22