Viscous Flow Design Project — Viscous Flow Code Optimization  
Consider the same fully developed turbulent flow in a channel that was solved in Assignment #8:
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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.
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%.
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