Students who complete this course will be able to:
- understand the most common techniques for the numerical solution of partial differential problems (such as finite differences and finite volumes),
- evaluate and comment on the stability and convergence of the numerical methods,
- and solve numerically diffusion, convection and transport problems in multiple dimensions.
Target Students: Students interested in solving partial differential equations numerically and in understating possibilities and limitations of numerical techniques. Students should have a general knowledge of partial differential equations.
Revision of numerical differentiation and integration.
Classification of PDE - elliptic, parabolic and hyperbolic equations.
Introduction to Python/MATLAB.
Finite difference method, convergence and stability.
Finite volume method.
Analogy with finite differences.
Method of characteristics.
System of partial differential equations.
Note on multiphase flows.
Final overview and questions
Students should have a general knowledge of partial differential equations. such as from the course B28.
A basic knowledge of Python, MATLAB or any other programming language is preferred but not essential.