====== Channelflow tutorial: using utility programs ======

===== Background =====

==== What is channelflow? ====
   * set of C++ libraries for high-level programming
   * set of command-line utility programs
   * set of matlab scripts for visualization
   * database of invariant solutions
   * website with documentation, discussion forums   

==== Why is CFD a hassle? ====
   * Navier-Stokes is a stiff, 3D, nonlinear, constrained PDE
   * Integration algorithms are complex, tailored to geometry
   * Turbulence has multiple scales, requires fine resolution
   * > 10^5-d state space, > 1 MB for each data point
   * Integration is computationally expensive
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 //this changes your workflow...// 
   * integrate a flow and save velocity field to disk at regular intervals
   * read saved data from disk for visualization, statistics, etc.
   * run jobs on number crunchers (PACE), transfer files via scp, ...
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//...and changes your analytic framework//
   * can't represent du/dt = F(u) simply
   * can't compute a 10^5 x 10^5 Jacobian matrix (even with sparse structure)
   * hard to choose projections for state-space portraits
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All this makes numerical analysis of fluid dynamics a hassle, compared to low-dimensional
ODE systems. 

Channelflow tries to lower the hassle factor by giving packaging important data structures
and algorithms and giving them simple, flexible, high-level interfaces:
   * in C++ classes, for writing your own fluids codes
   * in predefined utility programs, for common calculations
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We will discuss programming in channelflow another day.

Today is about using predefined channelflow utility programs to do calculations.

The utilities plus Matlab form a crude interactive system for CFD. 

===== Important concepts =====
==== FlowField ====

FlowField : C++ class representing spectral expansion of scalar, vector,
tensor fields

<latex>
  {\bf u}({\bf x},t) = \sum_{k_x k_y k_z} a_{k_x k_y k_z} T_{k_y}(y) \; e^{2 \pi i (k_x x / L_x + k_z z / L_z)}
</latex>

FlowField class has a platform-independent binary file format that retains 
coefficients, geometrical parameters, and other state information. We will discuss 
FlowField as a C++ class later, when we cover programming with channelflow. For, 
now, just think of a FlowField as a velocity field stored as a binary file (file 
extension .ff).

Why not ASCII? Binary floating-point IO is exact and much more efficient than
ASCII. Gives efficient, exactly invertible IO. Plus the ordering of multidimensional
spectral coefficients with complex symmetries is tricky enough that ASCII is 
incomprehensible, too. However, if you want ASCII values of velocity at each 
gridpoint, there's a utility for conversion (field2ascii).

In channelflow utilities, velocity fields u(x,t) are **differences from the laminar flow**

<latex>
{\bf u}_{total}({\bx x}, t) = {\bf u}({\bx x}, t) + y {\bf e}_x
</latex>

so that they have Dirichlet boundary conditions and form a vector space. The Matlab visualization
scripts add the laminar flow back on by default.

**Note: I moved the rest of this class tutorial into the ** [[docs:tutorial|channelflow tutorial]]. //John Gibson 2009-01-29//