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| MATI7122 | Numerical Mathematics in Fluids | 3+0+0 | ECTS:7.5 | | Year / Semester | Spring Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Prof. Dr. Selçuk Han AYDIN | | Co-Lecturer | Asst. Prof. Dr. Pelin ŞENEL | | Language of instruction | | | Professional practise ( internship ) | None | | | | The aim of the course: | | Gain the basic information about the fluid dynamic equations and ability to solve them numerically |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | Gain the basic information about fluid dynamics | 5 - 7 | 1,3,6, | | PO - 2 : | Learn the numerical methods for the solution of fluid dynamic problems | 5 - 7 | 1,3,6, | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| Mathematical derivation of computational fluid dynamics equations, stability and convergence analysis, basic information about numerical methods and to write computer programs for solving some computational fluid dynamics problems. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Introduction, Vector Calculus and Fluids | | | Week 2 | Mathematical basics of fluid dynamics and partial differential equations | | | Week 3 | Derivation of basic fluid dynamic equations and analysis | | | Week 4 | Basic numerical methods (Finite Difference and Finite Volume Methods) | | | Week 5 | Programming with Octave | | | Week 6 | Programming with Maxima | | | Week 7 | Finite Element Method and applications with FreeFEM | | | Week 8 | Lid driven cavity flow, step flow, flow around circle | | | Week 9 | MidTerm | | | Week 10 | Solutions of steady and unsteady convection-diffusion equation | | | Week 11 | Solution of the MHD Equations | | | Week 12 | Solution of the Burger's Equation | | | Week 13 | Solution of the Stokes Equation with MAC Algorithm | | | Week 14 | Navier-Stokes Equations and Artificial Compressibility Method | | | Week 15 | Solution of the Navier-Stokes equations in stream function and vorticity form | | | Week 16 | Final | | | |
| 1 | John D. Anderson, JR. Computational Fluid Dynamics, The Basics with Applications | | | |
| 1 | H.K. Versteeg and W. Malalasekera, An Introduction to Computatioanl Fluid Dynamics, Pearson, (Sec.Ed.) | | | 2 | G. Qin, Computatioanl Fluid Dynamics for Mechanical Engineering, CRC Press. | | | 3 | T.J. Chung, Computational Fluid Dynamics, Cambridge University Press, (Sec.Ed.) | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 16/04/2023 | 120 | 30 | | Homework/Assignment/Term-paper | 5
12 | 08/03/2023
15/05/2023 | 180
180 | 20 | | End-of-term exam | 16 | 20/06/2023 | 120 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 4 | 14 | 56 | | Arasınav için hazırlık | 6 | 1 | 6 | | Arasınav | 2 | 1 | 2 | | Ödev | 4 | 4 | 16 | | Dönem sonu sınavı için hazırlık | 8 | 1 | 8 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 132 |
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