Fluid mechanics and CFD
A pressure difference drives water through a channel. A moving wall drags it along. An obstacle redirects the flow and can leave an alternating wake. These are different consequences of the same mass and momentum balances.
This introductory book starts with predictions you can derive on paper. You
then read their mathematical ingredients in maintained .eqi sources, run the
existing cylinder investigation, and learn which conclusions the output supports.
Route through the book
Section titled “Route through the book”| Chapter | Question | Result you can check |
|---|---|---|
| 1. Continuum and statics | How can motionless water exert force? | Pressure depth law and gate load |
| 2. Mass, momentum and stress | What does a fluid region exchange with its surroundings? | Integral balances, Newtonian stress and energy loss |
| 3. Exact parallel flows | What fixes a velocity profile? | Couette and Poiseuille profiles, flux, shear and decay time |
| 4. Stokes flow and boundaries | Which assumptions and boundaries define the cylinder model? | Read the complete steady .eqi model |
| 5. Computing incompressible flow | How do equations become a computed field? | Run the steady example and design a refinement comparison |
| 6. Cylinder wakes | What changes when fluid carries its own momentum? | Interpret the transient workflow, vorticity and force histories |
First derive pressure, velocity profiles and time scales on paper. Then run the steady and transient cylinder examples. The final chapter connects the visible wake to forces, physical time and quantitative comparison.
What to bring
Section titled “What to bring”Start here if fluid motion is your interest. You need differentiation, elementary integration and vectors; we explain the stress tensor when it first appears. Use quantities and units and conservation laws as needed.
For computation, use the Linux x86-64 / CPython 3.13 source-install route in Get started, at the exact source revision linked by this site. Chapter 5 adds the mesh and plotting dependencies to that installation.
Connections
Section titled “Connections”Heat transfer uses the same storage–flux–source accounting, with energy instead of momentum. Viscosity diffuses momentum; thermal conductivity diffuses heat. Their coefficients and units differ. Structural mechanics shares traction and force balance, but an elastic solid relates stress to displacement strain whereas a Newtonian fluid relates viscous stress to velocity strain rate. Numerical simulation develops the error and time integration ideas used in Chapters 5 and 6.