M43071 Numerical hydrodynamics
This unit is designed to provide basic knowledge on computational
fluid dynamics and Navier-Stokes equations. We will study these equations
and various computational methods to solve them.
Syllabus:
Develop an understanding of basic methods in computational fluid
dynamics, numerical solution of one- and multi-dimensional parabolic,
elliptic and hyperbolic differential equations;
Be able to implement basic numerical methods for the computational fluid
dynamics;
develop programming skills in MATLAB/IDL/C++/Fortran
Lecture notes:
1 - Derivation of Navier-Stokes equations
2 - Finite differences #1, matrix form of FD equations
3 - Finite differences #2, stability, Lax convergence
4 - Finite differences #3, linear advection equation, von Neumann stability, CFL
5 - Finite differences #4, Lax-Friedrichs scheme, numerical diffusion
6 - Finite differences #5, 2nd order accurate Lax-Wendroff scheme
7 - Finite differences #6, Higher-order spatial schemes
8 - Finite differences #7, Higher-order temporal integration, Runge-Kutta schemes
9 - Finite differences #8, Higher-order temporal integration, Adams-Bashforth schemes
10 - Reynolds number, turbulence, direct Navier-Stokes simulations, large-eddy simulations
Homeworks:
Homework 1: numerical derivative
Homework 2: advection/continuity equation, instability
Homework 3: two-dimensional diffusion equation
Homework 4: Lax-Wendroff scheme for 1D linear advection
Homework 5: Full 1D hydrodynamics with Lax-Friedrichs scheme, Sod shock tube test
Homework 6: Full 2D hydrodynamics with Lax-Friedrichs scheme, Kelvin-Helmholtz instability
Homework 7: Full 2D hydrodynamics, Rayleigh-Taylor instability
Homework 8: Comparative analysis of numerical time integration schemes
