In order to demonstrate the capabilities of GENSMAC we present a number of calculations performed by the GENSMAC code as follows:

Two-dimensional Flows (Newtonian)

• 1. Numerical Simulation of container filling (square container): In this example we simulate the filling of a square container of dimensions 5 cm x 5cm with a inlet on the top side. The scaling parameters used in this example were: U = 1 m/s (inlet velocity), L = 6 mm (inlet size) and nu = 0.005 m^2/s. Figure 1 displays several snapshots taken from this example.
• 2. Sloshing: In this example we consider a block of fluid allowed to fall freely under gravity and slosh back and forth in a circular circular cavity. The scaling parameters for this example were U = 3.132, m/s (inlet velocity), L = 1 m and nu = 0.470 m^2/s. Figure 2 displays several snapshots taken from this run.
• 3. Jet Buckling: In this example we show the simulation of jet buckling. We consider a rectangular cavity with no-slip condition imposed on its wall. Through an inlet a thin jet of fluid is injected into the cavity at a constant velocity. The cavity is chosen to be sufficiently wide to permit buckling before the jet touching the side walls. The scaling parameters for this simulation were U = 1 m/s, L= 3 mm (inlet size) and nu = 0.01 m^2/s. Figure 3 displays several snapshots taken from this run.
• 4. Numerical Simulation of container filling (trapezoidal container): In this example we consider an open trapezoidal container and simulate the filling process of this container. The scaling parameters for this example were U = 1 m/s, L = 15 mm and nu = 0.0025 m^/s. Figure 4 displays several snapshots taken from this run.
• 5. Filling the `Foot' cavity: In this example we consider the `foot' cavity and inject Newtonian fluid in at the heel. No-slip conditions are imposed throught and gravity is neglected. The scaling parameters were chosen to be U = 5 m/s, L = 10 mm and nu = 0.025 m^2/s. Figure 5 illustrates several snapshots taken from this run.
• 6. Two-dimensional flow with symmetry: In this example we simulate the filling process of a rectangular container by specifying an axys of symmetry. The scaling paramenter for this run were U = 3 m/s, L = 4 mm and nu = 0.004 m^2/s. Figure 6 displays several snapshots taken from this run.

Axisymmetric Flows (Newtonian)

• 7. Filling of a circular container: In this example we simulate the filling process of a circular container. This is a typical example of axisymmetric free surface flow. Here we have an empty circular container and above it we set a circular nozzle from which a jet is jetted into the container at a prescribed constant velocity. The parameters used in this run were U = 1m/s, L = 0.01 m and nu = 0.005 m^2/s. Figure 7 displays several snapshots taken from this run.
• 8. Splashing drop: In this we simulate the splashing drop problem. We consider a circular tank full of fluid and above it a spherical drop with a constant initial velocity is let to fall freely into the tank under gravity. The scaling parameters for this run were U = 100cm/s (initial velocity of the drop), D = 3.2 cm (drop diameter) and nu = 3 cm^2/s (fluid viscosity). Figure 8 displays a number of snapshots from this run.
• 9. Filling a complex shaped container: In this example we simulate the filling process of a ``paint'' (glass for drinking beer). Figure 9 displays several snapshots from this run.
• 10. Jet flow experiment: In this example we simulate a jet impinging on a box o quiescent fluid. The importance of this calculation is that the results can be compared to the experimental results obtained by G. I. Taylor. In his experiment, Taylor observed that the jet bore into the fluid with a mushoom-like head formed at its front. The scalling parameters for this run we U = 0.5 m/s, D = 4 mm and nu = 0.0002 m^2/s (which gave a Re = 10). Figure 10 displays several snapshots taken from this run at different times.

Two-dimensional Flows (Non-Newtonian)

• 11. Numerical Simulation of container filling (square container-Cross model): Exactly the same problem as for example 1 (Newtonian) is considered except that the fluid now is non-Newtonian. We used the generalized Newtonian model with the viscosity being defined by the Cross model, that is, nu(q) is given by
• 
  nu(q) = nu_inf + (nu_0 + nu_inf)/(1 + (Kq)^m))

where q is the shear rate defined by

q = [2(du/dx)^2 + 2(dv/dy)^2 + (dv/dx + du/dy)^2]^(1/2)

The scaling parameters were the same as for example 1 and the viscosity was defined by

nu_inf = 0.001 m^2/s , nu_0 = 0.01 m^2/s, K = 4, m = 1.0

Figure 11 displays several snapshots taken from this simulation.

• 12. Filling of the Trapezoidal Container (Power-law fluid): Exactly the same problem as in example 4 is now considered except that the fluid is non-Newtonian. The model used is the generalized Newtonian with the power-law model, that is, the viscosity is given by

nu(q) = Kq^(n-1)

where the power-law was defined by

K = 5.829, n = 0.4415, q_min = 0.1898 s^(-1), q_max = 40.0 s^(-1), rho = 1214 kg/m^3.

Due to the high viscosity, we employed the Crank-Nicolson solver for computing the tilde velocities. Figure 12 displays several snapshots taken from this simulation.