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# Numerical Methods in Heat, Mass, and Momentum Transfer

Governing conservation equations and their classification according to numerical properties. Discretization by Taylor series, weighted residual, and control volume methods. Solution of systems of algebraic equations. Discretization and solution of the convection-diffusion equation. Methods of solving the equations governing fluid flow. Mathematical modeling of turbulence, combustion, and radiation.

## ME60800

3

### Learning Objective:

The course will cover fundamental aspects of Computational Fluid Dynamics (CFD) while providing exposure to the latest generation of high-level dynamic languages and version-control software. Students will be expected to write their own complete Navier-Stokes solver from scratch as a final project.

### Description:

Governing conservation equations and their classification according to numerical properties. Discretization by Taylor series, weighted residual, and control volume methods. Solution of systems of algebraic equations. Discretization and solution of the convection-diffusion equation. Methods of solving the equations governing fluid flow. Mathematical modeling of turbulence, combustion, and radiation. Sp2018 Syllabus

### Topics Covered:

1. Mathematical Description of Physical Phenomena
2. Overview of Numerical Methods
3. Diffusion Equation
4. Convection and Diffusion
5. Linear Solvers
6. Flow Field Calculation
7. Projects

### Prerequisites:

Prerequisites for the course include basic knowledge of fluid mechanics, linear algebra, partial differential equations and average programming skills. The use of Python is strongly recommended but not mandatory. The class content is structured in such a way to allow talented undergraduate students to successfully complete the coursework.

### Applied / Theory:

10 / 90

https://engineering.purdue.edu/ME608/webpage/

### Homework:

Bi-weekly assignments , typically consisting of 3-4 problems.

### Projects:

Students will be expected to write their own complete Navier-Stokes solver from scratch as a final project.

### Exams:

Quizzes and final exam

### Textbooks:

Official textbook information is now listed in the Schedule of Classes. NOTE: Textbook information is subject to be changed at any time at the discretion of the faculty member. If you have questions or concerns please contact the academic department.
No textbook is required. Notes will be provided.

### Computer Requirements:

ProEd minimum computer requirements.

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