7. Navier-Stokes#
Chapter 7 covers the Navier-Stokes equation and its key characteristics, as well as how to solve it numerically. The fully implicit solution to the NS equation will be derived, and a semi-implicit method (Pressure projection method) for solving the equation will be discussed. The lecture will also include some examples for demonstration. The learning objectives are as follows:
Derive an implicit discretisation for the NS equation
Derive a pressure projection discretisation for solving the NS equation
Derive appropriate boundary conditions for the problem
Learn how to implement a solver for the Pressure Poisson problem
Learn how to implement an explicit solver for the momentum equation, including the appropriate use of up-winding
Combine the solvers into a single Navier-Stokes solver capable of solving a range of fluid flow problems