Numerical Methods for Partial Differential Equations and Computational Fluid Dynamics

Numerical Methods for PDEs and Computational fluid dynamics (CFD) is a graduate-level course that applies numerical methods to partial differential equations, with particular application to the Navier-Stokes equations in fluid dynamics. The primary emphasis is on the use of finite-difference methods applied to elliptic and parabolic PDEs and incompressible flows. It covers the following topics:

Classification of partial differential equations
Finite-difference methods
Numerical solution techniques including direct, iterative, and multigrid methods for general elliptic differential equations
Numerical solution techniques including explicit and implicit methods for general parabolic differential equations, including numerical stability
Numerical algorithms for solution of the Navier-Stokes equations in the primitive-variables and vorticity-streamfunction formulations
Grids and grid generation
Numerical modeling of turbulent flows

A basic knowledge of numerical methods and fluid dynamics is assumed. The generic material on numerical methods applied to partial differential equations is from the book Matrix, Numerical, and Optimization Methods in Science and Engineering. The material on grid generation is from Variational Methods with Applications in Science and Engineering.