MATH596 COMPUTATIONAL BASIS OF FLUID DYNAM. EQ
| Course Code: | 2360596 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Prof.Dr. CANAN BOZKAYA |
| Offered Semester: | Fall Semesters. |
Course Objectives
At the end of this course, the student will:
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develop a deep understanding of the fundamental principles governing fluid motion
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derive and analyze the continuity, momentum, and energy equations for various flow regimes
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formulate and interpret the Navier-Stokes equations in different mathematical forms
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implement numerical solutions of fluid flow problems using finite difference methods
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assess stability, convergence, and accuracy of numerical schemes in fluid dynamics applications
Course Content
Introduction to fluid behavior. Derivation of continuity, momentum and energy equations. Navies-Stokes equations. Stream function, vorticity. Solutions of creeping, potential, laminar, boundary layer, turbulent flows. Solution of Navier-Stokes equations using finite difference methods in velocity-pressure , stream function-vorticity and stream function forms. Example solutions. Stability, convergence and error analysis.
Course Learning Outcomes
Student, who passed the course satisfactorily will be able to:
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derive the continuity, momentum, and energy equations from basic physical principles
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explain the role of stream function and vorticity formulations in two-dimensional incompressible flows
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classify and analyze different flow regimes such as creeping, potential, laminar, turbulent, and boundary layer flows
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construct numerical schemes for solving Navier-Stokes equations in velocity-pressure, stream function-vorticity, and stream function formulations
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implement finite difference methods for solving canonical fluid dynamics problems and validate the results
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perform stability, convergence, and error analysis for numerical solutions in computational fluid dynamics
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critically interpret the physical and numerical results of selected benchmark flow problems
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields. | ✔ | |||
| 2 | Gains academic maturity through self-study. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Carries out parts of a mathematical research program independently. | ✔ | |||
| 5 | Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak). | ✔ | |||
| 6 | Contributes to solving global, environmental and social problems either individually or as being part of a social group. | ✔ | |||
| 7 | Respects ethical values and rules; applies them in professional and social issues. | ✔ | |||
| 8 | Can work cooperatively in a team and also individually. | ✔ | |||
| 9 | Gets exposed to academic culture through interaction with others. | ✔ | |||
| 10 | Comprehends necessity of knowledge, can define it and acquires it; uses knowledge effectively and shares it with others. | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution