This lecture starts with the basic concepts of fluids, flows and heat transfer. The components and properties as well as the limitations of numerical methods are then addressed, where different discretization approaches are examined. The fundamental principles of finite difference methods and finite volume methods are subsequently introduced followed by the investigation of various approaches for solving the linear equation systems. The time-marching methods for unsteady flow and heat transfer problems are surveyed, whereas the solution methods for the Navier-Stoke equations are demonstrated. The turbulent and compressible flow problems are also discussed together with the grid issues arising from complex geometries. The strategies for improving the computational efficiency and accuracy are reviewed. Hand-on hours of PDE solver platform and commercial CFD software are employed to the application of the principles of finite volume methods to the fluid dynamics and heat transfer problems.

Students are targeted to understand the fundamental principles of the finite volume methods and to be capable of applying the finite volume methods to the fluid dynamics and heat transfer problems.

programming language, numerical analysis, fluid mechanics, heat transfer

6 hours

1. F. Moukalled, L. Mangani, M. Darwish, The finite volume method in computational fluid dynamics: an advanced introduction with OpenFOAM, Springer, 2016. 2. Pradip Dutta and Suman Chakraborty, Finite-Volume Method for Numerical Simulation: Fundamentals, CRC press, 2012. 3. Randall J. LeVeque, Finite volume methods for hyperbolic problems, Cambridge University Press, 2002. 4. Joe E. Thompson, Z.U.A. Warsi and C. Wayne Mastin, Numerical Grid Generation: Foundations and Applications, Elsevier, 1985. 5. Dale Arden Anderson, John C. Tannehill, Richard H. Pletcher, Computational Fluid Dynamics and Heat Transfer, Hemisphere Publishing, 1984.

Joel H. Ferziger, Milovan Perić, Robert L. Street, Computational Methods for Fluid Dynamics, 4th ed., Springer, 2020.