MAK563

School of Engineering \ Mechanical Engineering

3

9

Elective

Turkish

-

Classification of partial differential equations. Finite-difference formulation. Stability analysis. Parabolic partial differential equations. Elliptic partial differential equations. Hyperbolic partial differential equations. Navier-Stokes equations: Scalar representation of Navier-Stokes equations, incompressible Navier-Stokes equations. Boundary conditions. Euler equations. Network generation: Structured and unstructured networks.

Textbook:
"Computational Fluid Dynamics", Hoffmann, Klaus A., Engineering Education System, 2000.

Other Sources:
1. "Computational Fluid Dynamics: The Basics with Applications", Anderson, John D., McGraw-Hill, 1995.
2. "Computational Fluid Mechanics and Heat Transfer", Tannehill, Anderson, and Pletcher, , 2nd Edition, 2002, ISBN: 0071235671.

Numerical modeling of the equations of motion of fluid dynamics and their initial- and boundary-conditions. Solution of matrix numerical methods applied to model fluid equations. Concepts of numerical algorithms such as numerical decomposition, error bounds, convergence, stability, accuracy and robustness. Solution, processing and validation of flow problems with computer hardware and software tools.

1. Acquisition of the ability to numerically model the fundamental equations of fluid dynamics.
2. Derivation of appropriate numerical algorithms for solving the modeled equations according to the physical and mathematical nature of the equations.
3. Application of matrix numerical analysis methods for the solution of the equations.
4. Display and interpretation of the results by using computerized graphical techniques.

Week 1: Numerical Fluid Dynamics. Equations of fluid dynamics.
Week 2: Classification of partial differential equations. Finite-difference formulation.
Week 3: Classification of partial differential equations. Finite-difference formulation.
Week 4: Parabolic partial differential equations. Elliptic partial differential equations.
Week 5: Hyperbolic partial differential equations. Stability analysis.
Week 6: Navier-Stokes equations.
Week 7: Navier-Stokes equations.
Week 8: Euler equations.
Week 9: Vorticity - Stream Function formulation
Week 10: Coordinate transformation, Jacobian and metrics. Boundary conditions.
Week 11: Network generation: Structured networks.
Week 12: Network generation: Unstructured networks.