## Two Nodes Coupled by a Link

**Method of Exact Solutions Verification Problems for Transient Compressible Flows: Two Nodes Coupled by a Link**

The analysis given in these previous notes:

Implicit Function Theory Introduction

Initial Method of Exact Solutions Calculations

Single Isolated Node Calculations

Two Fluid Systems Mechanically Coupled Through a Wall

are expanded to include the case of two fluid nodes coupled by a link. Numerical and analytical solutions results are given for an illustrative application.

The mathematical model, an exact continuous analogue of the discrete approximations used in many numerical solution methods, provides analytical and numerical-benchmark problems for verification by the Method of Exact Solutions ( MES ).

I have uploaded a file.

## Fluid Systems Mechanically Coupled Through a Wall

**Method of Exact Solutions Verification Problems for Transient Compressible Flows: Two Fluid Systems Mechanically Coupled Through a Wall**

The analysis given in these previous notes:

Implicit Function Theory Introduction

Initial Method of Exact Solutions Calculations

Single Isolated Node Calculations

are expanded to include the case of coupled fluid systems. Numerical solution results are given for an illustrative application.

The mathematical model, an exact continuous analogue of the discrete approximations used in many numerical solution methods, provides analytical and numerical-benchmark problems for verification by the Method of Exact Solutions ( MES ).

I have uploaded a file.

## 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.

## Looks like we’re getting some Traction

This is interesting; Computational science: …Error. From *Nature News*, even. Comments allowed over there.