course outline - The Ohio State University
Transcription
course outline - The Ohio State University
MECHENG 6507: Intermediate Numerical Methods Spring Semester, 2014 The Ohio State University Scott Lab E0141 TuTh 3.55 pm — 5.15 pm Instructor Dr. Sandip Mazumder Room E410, Scott Laboratory Phone: 247-8099 Email: [email protected] Office Hours Room E410, Scott Laboratory, preferably by appointment, or walk-in. Feel free to call instructor at home (614-442-5957) or on his cell phone (256-658-5004). No calls after 10 pm please. Textbook/ Reading Material There is no required text for this course. References for Supplementary Reading Numerical Mathematics and Computing, W. Cheney, and D. Kincaid, Second Edition, 1985, Brooks Cole Publishing Company, ISBN 0534043569 Numerical Solution of Partial Differential Equations: Finite Difference Methods, G.D. Smith, Third Edition, 1985, Clarendon Press (Oxford), ISBN 0198596413 Numerical Heat Transfer and Fluid Flow, S.V. Patankar, 1980, Hemisphere Publishing Corporation, ISBN: 0891165223 Website Go to ME/NE 6507 website on Carmen (carmen.osu.edu). Please check the website at least twice a week for updates. Lectures Lecture notes (slides) will be posted on Carmen prior to the lecture. Students are encouraged to print them out and bring to class. Lectures will also be recorded, and a link to the video will be posted on Carmen approximately within 24 hours following the lecture. Prerequisites The instructor will assume that you are familiar with course material covered in undergraduate numerical methods (ME 250 or equivalent). You will be expected to write computer programs during the course and therefore, must be familiar with at least one computer language, such as Fortran, Pascal, C/C++, or Matlab. If you are not familiar with any programming language, you are advised to drop out of the course. If you use Matlab, you are allowed to use it as a programming environment only. Use of Matlab in-built functions, unless otherwise stated, is strictly prohibited in this course. Grading Policy Homeworks: 60% Midterm Exam (in class): 20% Final Exam (in class): 20% Tentative Grading Scale 90% and above: A 80% to 90%: A70% to 80%: B+ 60% to 70%: B 50% to 60%: BBelow 50%: C Note: The above grading scale is meant to serve as a guideline, and may be shifted up or down. Academic Misconduct Please read http://studentaffairs.osu.edu/resource_csc.asp to understand your responsibilities as a student. Failure to abide by the rules stated in this section is severely punishable by the University. Homework Policy All homeworks will involve computer programming. You must submit a printout of your program with the homework write-up. Even if your program is not working, you are encouraged to submit it to earn partial credit. No late homework will be accepted, unless you are seriously ill. Any attempt at using someone else’s program will be severely penalized, including expulsion from the course. Electronic submission of homeworks is strongly discouraged. If you submit an electronic copy, it must be submitted as a single self-contained PDF or MSWord file, and must not contain any plots in color. No other format will be accepted. Absence from Examination If you do not appear for an examination without advance notice, you will automatically receive a zero grade. Makeup exams will be entertained only if the instructor is notified at least one week in advance. Examinations Both examinations will be open book/notes and in class. The format of the examination and other relevant details will be discussed in class prior to the examination. Policy on Seeking Help On many instances, you may require the instructor’s help to debug programs. To get help, you must meet the instructor in person with either a hard copy of your program or the program on a laptop/tablet (the latter is preferred). E-mails to the instructor stating that the program does not work (with attached program) and a request to look at it will be ignored. The instructor will not debug or run your program. That is the students’ responsibility. Tentative Syllabus and Course Schedule This course is intended to introduce students to the finite-difference and finite-volume methods for solving canonical partial differential equations encountered in engineering. Students interested in the finite-element method should take ME 5168. Date 1/7 (Tu) 1/9 (Th) 1/14 (Tu) 1/16 (Th) 1/21 (Tu) 1/23 (Th) 1/28 (Tu) 1/30 (Th) 2/4 (Tu) 2/6 (Th) 2/11 (Tu) 2/13 (Th) 2/18 (Tu) 2/20 (Th) 2/25 (Tu) 2/27 (Th) 3/4 (Tu) 3/6 (Th) 3/18 (Tu) 3/20 (Th) 3/25 (Tu) 3/27 (Th) 4/1 (Tu) 4/3 (Th) 4/8 (Tu) 4/10 (Th) 4/15 (Tu) 4/17 (Th) 4/28 (M) Topics Covered/Major Deadlines Introduction, classification of PDEs General discussion of methods for solving PDEs, types of meshes used etc., Derivation of finite-difference equations in 1D Errors in difference approximations, application of boundary conditions, matrix setup Gaussian elimination, solution to tri-diagonal and other banded systems Treatment of non-linear sources, residual calculation, solution of coupled non-linear algebraic equations using Newton’s method Finite-difference in 2D, sparse systems, introduction to iterative solvers, Jacobi method Gauss-Seidel method, successive over-relaxation (SOR), line-by-line methods (ADI). Incomplete LU decomposition, pre-conditioning: basic philosophy, Stone’s strongly implicit method (SIP) Method of steepest descent, conjugate gradient (CG) method Correction form of equations, inertial damping, convergence analysis of various iterative methods, Fourier decomposition of errors Spectral radius of convergence and calculation procedure Convergence analysis continue for various schemes Multi-grid methods, basic philosophy, geometric multi-grid (GMG) Multi-grid methods continued, algebraic multi-grid (AMG) Summary of linear algebraic equation solvers MIDTERM EXAMINATION Errors in difference approximations re-visited, higher-order methods Parabolic problems, time marching, forward and backward Euler methods, CrankNicholson method, stability vs. accuracy Parabolic problems continued…, higher order explicit methods Cylindrical coordinate system Finite-volume method (FVM), basic philosophy, difference between FVM and FDM FVM continued… Finite-volume integration of elliptic PDEs on unstructured mesh, general formulation, geometry calculations Boundary conditions for unstructured FVM Unstructured mesh continued…, code development details Hyperbolic PDEs, key issues, fluid flow, introduction to Euler and Navier-Stokes Equations Miscellaneous topics (TBD) Miscellaneous topics (TBD) FINAL EXAMINATION, 6.00 to 7.45 pm