Reference no: EM132276851 , Length: word count:2000
Computational Thermo-Fluids Assignment -
CP2 - ITERATIVE METHODS FOR SOLUTION OF STEADY AND UNSTEADY 2D HEAT CONDUCTION PROBLEMS USING NUMERICAL INTEGRATION OF FDM EQUATIONS
Objectives -
- After completing this CP, the students should be able to evaluate positive and negative features of four basic terative integration algorithms (Jacobi, Gauss-Seidel, SOR, SLOR) as it applies to FDM method on uniform orthogonal grid for the solution of the LaPlace's equation governing steady temperature field in a rectangular plate made of an isotropic material.
- Plot converged temperature fields for each of the four iterative methods used. You might want to use MATLAB plotting capability as described in the folder in the DROPBOX that is called PROGRAMMING AND COMPUTER STUFF.
- Convergence histories of the four algorithms should be plotted on the same figure as log(10) of the maximum error versus number of iterations.
- Influence of the value of the over-relaxation parameter omega in PSOR and SLOR should be analyzed by creating a figure showing the number of iterations needed to achieve convergence versus the value of omega.
- Influence of the grid refinement should be analyzed by first running the code on a relatively coarse grid (for example, xcells = 10, ycells = 20) and then repeating the calculations on a refined grid (for example, xcells = 20, ycells = 40), etc..
- Field plots of the converged temperature fields should also be created and discussed.
Tasks -
1. Read this entire statement carefully.
2. Read reports from previous students that worked on the same project. Please understand that reports from the previous students and software provided by them are not necessarily correct nor complete. These reports only have the purpose to help you learn this material faster and submit a more correct and complete report.
3. Check the FORTRAN program provided. It requires you to input each variable by typing on your computer. This code has options to use any of the these iterative algorithms: Jacobi, Gauss-Seidel, PSOR, LSLOR, ADI.
4. Compile the code using a FORTRAN compiler and then run the code for each of these iterative methods.
5. Repeat the runs by varying different input parameters (such as icells, jcells, etc.).
6. Write a detailed report. This report must include a complete MSWord file including all pertinent formulas processed using EquationEditor, background text, descriptions of the work performed, tabulated conditions for all test cases/modifications studied, figures showing all pertinent aspects of each problem studied, discussion of each result, conclusions/recommendations, and detailed pertinent references. The zipped file should also involve all pertinent computer codes, their input files, and pertinent output files.
7. Your complete report (it must be completely word-processed) must includes:
- your cover sheet,
- this TASKS page,
- summary,
- nomenclature,
- introduction/background/description of steps used to run the software,
- all pertinent equations (numbered),
- detailed graphical results (numbered),
- detailed discussion of the results,
- recommendations for future research,
- pertinent references used, and
- files of all inputs, source codes, and outputs.
Plot the results using any common computer graphics software (e.g., MATLAB).
Use different types of lines or symbols to plot results on the same figure.
Your CP report must also have a detailed listing of the compter code and inputs.
Your report should look like a professional, single-column technical paper.
This final report should be a .doc file. Also, create its .pdf version.
Word count : 2000 including calculations if required.
Attachment:- Assignment Files.rar