Did you check if your answer is grid-converged? I.e., if changing $N$ by 2 times does not result in a major change in $u_b$?
 12.04.17
 Question by Student 201327103 I get appropriate answer at $N=29-30$, but i have to start at 100 and doubling the N. 100 is too big to $u_b$. why this happen?
First, make sure you use $N=5000$ (or more) to test your algorithm properly. Then, is the answer converged? I.e, are you getting the same answer for $N=20000$ then for $N=5000$?
 Question by Student 201327103 No, the answer is bigger with larger N. Something going wrong.
You mean your answer is not converging? If so, then there's something wrong with your coefficients somewhere. Comment out some terms and check if your answer becomes independent of $N$ (very important whether the answer is right or wrong). If yes, then it means the problem is somewhere within the terms you commented.
 Question by Student 201327107 Professor, I have a question about $\tau_w$. Should $\tau_w$ be treated as a constant instead of a variable? And do I have to take the absolute value of $\frac{\partial u}{\partial y}$ where $\tau_w=(\mu+\mu_t)\frac{\partial u}{\partial y}$
You don't need to take the absolute value but $\tau_w$ should be positive anyway. If it isn't, this means there's a bug somewhere. You should treat $\tau_w$ as a constant within one iteration only (i.e. because find_coeff_and_rhs is called once at each iteration, thus $\tau_w$ should be taken as constant within find_coeff_and_rhs). Of course, it should be updated every time find_coeff_and_rhs is called..
 Question by Student 201427102 professor, thank you for teaching 'malloc and *'. I changed initial conditions and wrote some eqs to get yplus and mut. After run my code, yplus values are symmetry and same as in class. But mut don't update. why do not mut update?

 12.05.17
Hm does mut equal 0 for all nodes?
 Question by Student 201427102 Surprisingly, Yes it does. even I changed 'void init_u_mut(long N, double *u, double *mut)' , mut always equals 0.
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