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2024　Fundamentals of computational mechanics 1

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Academic unit or major
Undergraduate major in Mechanical Engineering
Instructor(s)
Onishi Ryo  Kodama Manabu 
Class Format
Lecture / Exercise    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
-
Group
1
Course number
MEC.B222
Credits
2
Academic year
2024
Offered quarter
4Q
Syllabus updated
2024/4/1
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

Numerical simulations are useful in solving mathematical problems in practical fields and thus used in research and development in various fields of mechanical engineering. For example, matrix calculations and numerical solutions of differential equations are used not only in mechanical engineering but also in a wide range of science and engineering fields. Owing to the development of analytical techniques, these simulations can be attained by using general-purpose simulators. However, in order to obtain correct analysis results or to deepen understanding of the phenomena to be handled, it is necessary to learn the principle of operation.
　In this lecture, as a foundation of numerical computation, the objective is to understand the basic concepts of numerical simulation methods, to create and run actual computation programs, and to acquire the skills to actually utilize numerical simulation.

Student learning outcomes

In this course, students will acquire the following contents.
1. to understand errors in numerical computation, various methods for solving linear systems of equations, nonlinear equations, and the difference method, which are basic methods for numerical computation.
2. to be able to apply the above methods to ordinary differential equations and partial differential equations of actual problems
3. to be able to write calculation programs by oneself and solve actual problems.

This course is designed to meet the following objectives
6. developmental expertise in mechanical engineering
7. the ability to solve new problems and make creative proposals by utilizing specialized knowledge

Keywords

Computational Mechanics, python language, simultaneous linear equations, nonlinear equations, explicit method, ordinary differential equations, difference method, Courant number, numerical viscosity, partial differential equations, advection equations, diffusion equations

Competencies that will be developed

✔ Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills
✔ This class aims at learning 6 and 7 of learning objective.

Class flow

In the first half of the lecture, the principles and programming methods of each method will be explained, and in the second half, exercises related to the principles and programing will be created.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Overview of numerical computation and computer technology, confirmation of programming environment, and execution of calculations To understand the purpose of learning numerical computation methods and examples of state-of-the-art computations. To build an environment to execute calculations, to understand the difference between C and python, and to learn python programming.
Class 2 Vector and matrix calculations, solution of simultaneous linear equations (direct method) Understand matrix calculations, Gaussian elimination, and learn to solve simultaneous linear equations by the direct method.
Class 3 Solution of simultaneous linear equations (iterative method) and summary Understand the SOR method and the steepest descent method, and learn how to solve simultaneous linear equations by the iterative method.
Class 4 Numerical solution of ordinary differential equations Acquire numerical solution methods for ordinary differential equations by explicit methods.
Class 5 Numerical solution of advection equations Understand the principles of the difference method, spatial discretization, upwind difference method, Courant number, and numerical viscosity, and learn to solve advection equations numerically.
Class 6 Numerical solution of diffusion equations To understand the boundary conditions in the concentration-diffusion equation and the heat conduction equation, and to acquire numerical solution methods for the diffusion equation.
Class 7 Numerical solution practice for partial differential equations To acquire practical numerical solution methods for partial differential equations such as advection-diffusion equations.

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 30 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course materials.

Textbook(s)

None in particular (lecture materials will be distributed prior to the lecture. Additional materials will be distributed during the lecture.)

Reference books, course materials, etc.

You can find a wide variety of resources on the Internet. If you want something systematic, for example, you can refer to the following.
Feng Xiao and Takao Nagasaki, "Fundamentals of Numerical Fluid Analysis," Corona Publishing Co.
Masatake Mori, "Numerical Analysis (2nd Edition)", Kyoritsu Shuppan
Tetsuro Yamamoto, "Introduction to Numerical Analysis [Revised Edition]," Science Inc.

Assessment criteria and methods

Comprehensive evaluation will be based on in-class exercises (40%) and a final examination (60%).

Related courses

  • MEC.B201 ： Fundamentals of information and mathematical sciences
  • MEC.K332 ： Finite Element Analysis

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Bring your own laptop PC; basic knowledge of C is required; basic knowledge of Python is also desirable.

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