A straight interface is advected by a pure shear flow. The exact solution is simply a rotation of the interface around the center of the box. Note that both the interface and the velocity field should be described exactly by a second-order method.
Figure 41 illustrates what happens when using a VOF scheme to follow the interface. The green segments are the VOF-reconstructed interface obtained when using a "naive" Eulerian PLIC method. The red segments are the VOF-reconstructed interface obtained when using a "multiband" Eulerian PLIC method (with n = 4 bands).
Figure 42 illustrates the evolution of the error with time. For t=1 the interface is at 45 degrees and the errors in fluxes cancel out exactly.
(a) (b) (c) (d)