Viscous Flow Design Project — Viscous Flow Code Optimization
Consider the same fully developed turbulent flow in a channel that was solved in Assignment #8:
Now, improve the Prandtl algebraic code that you wrote in Assignment #8 and submit a new final code that makes the following ratio as high as possible: $$\Phi=\frac{1}{N \times n}$$ In the latter, $N$ is the number of nodes and $n$ is the number of iterations needed to obtain convergence. To maximize $\Phi$, consider making the following changes:
 (a) Take advantage of the symmetry of the problem: reduce the domain from $0\le y \le 2 H$ to $0 \le y \le H$ by imposing a symmetrical boundary condition at $y=H$. (b) Implement variable grid spacing and cluster more nodes near the wall than near the axis of symmetry. (c) Adjust the relaxation factor for optimal convergence rates (d) Use higher-order polynomials to extrapolate the properties at the cells interfaces.

 07.01.16
 Notes
 1. The number $n$ must correspond to the number of iterations needed for all properties to reach a relative error of $10^{-7}$. I.e., in the code, relerrmax must be set to 1E-7. 2. The parameter $\Phi$ must be obtained for a “grid converged” solution. That is, you must demonstrate that should $N$ be divided by 2, the bulk velocity $u_{\rm b}$ does not vary by more than 1%.
 07.17.16
 Due on December 16th at 4pm.
 12.06.17
 $\pi$