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.
Elliptic equations.
Finite difference method, convergence and stability.
Parabolic equations.
Iterative methods.
Finite volume method.
Analogy with finite differences.
Hyperbolic equations.
Method of characteristics.
System of partial differential equations.
Navier-Stokes 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.