Models Methods Software

Implicit Function Theory Applications; Part 1: Method of Exact Solutions

In a previous post I gave some background info about implicit function theory and how it might be useful. In these notes I have used results from applications to the equation of state to develop a few exact solutions for extremely simple transient, compressible flows that include fluid-structure interaction. These notes address the case of mechanical coupling of the fluid to a deformable / flexible wall. I have also included an introduction to the case of coupling of fluid systems through a common deformable / flexible wall. Additional notes will address the case of thermal interactions for both a single fluid system and coupled systems.

I kind of ran out of steam when I got to coupled-systems part of the present notes. There’s a lot of ground to cover for this case and I’m thinking a separate report might be the way to go. With coupled systems you get more that just twice as many things to look at compared to the single-system case.

I think these solutions might be candidates for analytical, and numerical-benchmark-grade, Method of Exact Solutions ( MES ) for verification of limited aspects of coding of transient compressible fluid flow model equation systems and solution methods.

I have uploaded a file.

Consider these notes as a rough draft of a report and let me know what you think about all aspects.

January 19, 2011 - Posted by Dan Hughes | Calculation Verification, Verification | Numerical methods Verification, Numerical Solution Methods, ODEs, Software Verification, Verification