09 – Falling Block

In this exercise, students simulate the motion of a dense block sinking in a viscous fluid under the influence of gravity. The problem is set up in two dimensions with constant viscosity (isoviscous case) and free-slip velocity boundary conditions on all sides.

The goals of this exercise are to:

• Set up the 2-D model geometry and define the block phase within the background medium.
• Assign appropriate physical parameters, such as viscosity, density contrast, and gravity.
• Implement the momentum and mass conservation equations using the finite difference method.
• Assemble and solve the resulting linear system of equations for velocities and pressure.
• Visualize the velocity field and the interaction between the sinking block and the surrounding viscous medium.

This exercise provides a simple but powerful benchmark problem to validate the Stokes solver and to understand the dynamics of density-driven flow in an isoviscous medium.