This course will provide students with an introduction to numerical methods and MATLAB®. Topics covered throughout the course will include: errors, condition numbers and roots of equations; Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis, and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; Lagrangian Coherent Structures. Subject includes a final research project.
The specific objectives of the course are:
- To introduce and develop the main approaches and techniques that constitute the basis of numerical fluid mechanics for engineers and applied scientists.
- To familiarize students with the numerical implementation of these techniques and numerical schemes, so as to provide them with the means to write their own codes and software, and so acquire the knowledge necessary for the skillful utilization of CFD packages or other more complex software.
- To cover a range of modern approaches for numerical and computational fluid dynamics, without entering all these topics in detail, but aiming to provide students with a general knowledge and understanding of the subject, including recommendations for further studies.
This course continues to be a work in progress. New curricular materials are being developed for this course, and feedback from students is always welcome and appreciated during the term. For example, recitations and reviews on specific topics can be provided based on requests from students.
课程影音（Audio and Video）