When fluid-structure interaction (FSI) is solved as a loosely coupled problem we face the risk of applying unphysical boundary conditions. The fluid domain is unaware of the constraint of the structural domain and vice versa. Imagine an elastic container with inlets only. When the fluid is incompressible the continuity equation is unphysical as the net flux inside the domain is not constant.

The above mentioned problem may be solved by introducing an artificial incompressibility for the fluid that accounts for the elasticity of the structural boundaries. In the following examples the artificial compressibility method is applied to the incompressible Navier-Stokes equations.

• A square with one elastic wall is being filled from the opposite wall, velocity: gif, mpg, pressure: mpg, mesh: mpg.
• A container with one elastic wall and sinusoidal neck being filled, velocity: gif, mpg, pressure: mpg, mesh: mpg.
• A cube with one elastic wall is being filled from the opposite wall, velocity: jpg, mpg.
• A square with two elastic walls is being filled from the third wall, velocity: gif, mpg, pressure: mpg.
• The space between two elastic sheets is filled and emptied from one end, gif, mpg.
• As the previous case except now the fluid may freely flow out of the system from the other end, gif, mpg.
• Pressure pulse in a cylindrical vessel, mpg.