Lab 8&9

Issues in the numerical simulation of the lid-driven cavity

Use the script cavity.m to solve the Navier-Stokes equations in a lid-driven cavity:

a) Plot the streamlines in the cavity at increasing # of CVs, for Re = 1000;

Use the script cavity.m to solve the Navier-Stokes equations in a lid-driven cavity:b) Plot the velocity profiles at the vertical centerline of the cavity at increasing # of CVs, for Re = 1000;

Use the script cavity.m to solve the Navier-Stokes equations in a lid-driven cavity:c) Plot the streamlines in the cavity at different Re for a given # of CVs;

In this case: CV = 60x60

Use the script cavity.m to solve the Navier-Stokes equations in a lid-driven cavity:d) Plot the velocity profiles at the vertical centerline of the cavity at different Re for a given # of CVs; In this case: CV = 60x60

Use the script cavity.m to solve the Navier-Stokes equations in a lid-driven cavity:

e) For Re = 1000, check the convergence of the algorithm on the strength of the primary and secondary vortices as a function of the # of CVs, and on the mesh spacing, trying to use also different spatial discretization schemes;

Use the script cavity.m to solve the Navier-Stokes equations in a lid-driven cavity:

f) For Re = 1000 and for a staggered 32x32 CV grid, plot the number of outer iterations required to reduce the residual level in all equations by three orders of magnitude, as a function of αP (and for different values of αu). Redo the study for a colocated grid.

Use the script cavity.m to solve the Navier-Stokes equations in a lid-driven cavity:

g) For Re = 1000 and for a staggered 32x32 CV grid, plot the number of outer iterations required to reduce the residual level in all equations by three orders of magnitude, as a function of α U. Redo the study for a colocated grid.