Fluid Mechanics: Fundamentals and Applications
Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 15, Problem 9CP
To determine

(a)

The multigridding used by CFD codes to speed up the iteration process.

To determine

(b)

Artificial time used by CFD codes to speed up the iteration process.

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Suppose your CFD code can handle nonelementary blocks. Combine as many blocks of Fig. as you can. The only restriction is that in any one block, the number of i-intervals and the number of j-intervals must be constants. Show that you can create a structured grid with only three nonelementary blocks. Renumber all the blocks and indicate how many i- and j-intervals are contained in each block. Add up all the cells and verify that the total number of cells does not change.
The following tools / resources may be useful for you to complete the assignment:a. Chatgpt (You may use it to learn Matlab coding or any other computer language. An example is given here: https://shareg.pt/mXHGne9 ). Please take note that code generated by chatgpt can be directly copied and pasted.b. Matlabi) Useful cheat sheet (https://n.ethz.ch/~marcokre/download/ML-CheatSheet.pdf)ii) Getting started with Matlab (https://matlabacademy.mathworks.com/en/details/gettingstarted )iii) Getting 30-day Matlab trial license (https://www.mathworks.com/campaigns/products/trials.html ) iv) Polyfit (https://www.mathworks.com/help/matlab/ref/polyfit.html )v) Exponential Fit (https://www.mathworks.com/matlabcentral/answers/91159-how-do-i-fit-an-exponential-curve-to-my-data)c. PlotDigitizer (https://plotdigitizer.sourceforge.net/ ) or a free online app that does not requires installation (https://plotdigitizer.com/app )You may use your own engineering judgement to make any assumptions on any…
We have designed a divide-and-conquer algorithm that runs on an input of size n. This algorithm works by spending O(1) time splitting the problem in half, then does a recursive call on each half, then spends O(n2 ) time combining the solutions to the recursive calls. On small inputs, the algorithm takes a constant amount of time. We want to see how long this algorithm takes, in terms of n to perform the task. (a) First, write a recurrence relation that corresponds to the time-complexity of the above divide and conquer algorithm. (b) Then, solve the relation to come with the worst-case time taken for the algorithm. Please show all work in depth.
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