Numerical methods for fluid mechanics, heat and mass transfer

9:00-10:30           Numerical methods for the heat conduction equation and diffusion problems:

                               The forward in time central in space method (FTCS)

                               The backward in time, central in space method (BTCS)

10:30-11:00        Coffee break

11:00-12:30        Numerical methods for the linear scalar advection equation and nonlinear scalar conservation laws

                               The explicit upwind method for the linear scalar advection equation: discussion and analysis  

                               The Riemann problem and the Godunov method for nonlinear scalar conservation laws  

12:30-14:00        Lunch break

14:00-17:00        Practical computer laboratory exercises on numerical methods for convection and diffusion problems

 

 

9:00-10:30           Numerical methods for the incompressible Navier-Stokes equations

                               Discussion of the governing PDE

                               Semi-implicit schemes on staggered grids for the discretization of the incompressible Navier-Stokes equations with scalar transport and buoyancy forces due to temperature gradients

10:30-11:00        Coffee break

11:00-12:30        Practical computer laboratory exercises on semi-implicit schemes on staggered grids for the discretization of the incompressible Navier-Stokes equations with scalar transport and buoyancy forces due to temperature gradients

12:30-14:00        Lunch break

14:00-17:00        Practical computer laboratory exercises on semi-implicit schemes on staggered grids for the discretization of the incompressible Navier-Stokes equations with scalar transport and buoyancy forces due to temperature gradients

                               Test case: natural convection in a closed heated cavity with additional scalar transport