2025 (Current Year) Faculty Courses School of Engineering Undergraduate major in Mechanical Engineering
Fundamentals of computational mechanics
- Academic unit or major
- Undergraduate major in Mechanical Engineering
- Instructor(s)
- Ryo Onishi / Manabu Kodama
- Class Format
- Lecture/Exercise
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Class
- -
- Course Code
- MEC.B222
- Number of credits
- 110
- Course offered
- 2025
- Offered quarter
- 4Q
- Syllabus updated
- Mar 19, 2025
- Language
- Japanese
Syllabus
Course overview and goals
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.
Course description and aims
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
- 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/Objectives
| Course schedule | Objectives | |
|---|---|---|
| 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. |
Study advice (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.
A variety of materials can be found on the Internet.
For the latter half of the lecture, it is advisable, but not required, to purchase the following books for reference.
藤井孝藏 (著), 立川智章 (著)『Pythonで学ぶ流体力学の数値計算法』オーム社
Evaluation methods and criteria
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
Bring your own laptop PC; basic knowledge of C is required; basic knowledge of Python is also desirable.