A test case initially presented by Rudman . A circular patch of tracer is advected in a vortical shear flow. At t = 2.5 the flow direction is reversed. An exact advection scheme would restore the initial circular shape at t = 5.
The VOF (Volume-Of-Fluid) advection scheme is not exact. The initial, intermediate and final shape of the interface are represented on Figure 35. Figure 36 illustrates the error between the initial and final shapes. The corresponding error norms are given in Table 1.
Adaptive refinement is used with the gradient of the volume fraction as criterion. Eight levels of refinement are used on the interfaces and six away from the interface.
(a) (b) (c)
L1 L2 L∞ 1.734e-04 5.716e-03 3.770e-01 1.734e-04 5.716e-03 3.770e-01
Same as the previous test but with adaptivity based on the local curvature of the interface (with a maximum of eight levels of refinement).
L1 L2 L∞ 1.021e-03 1.143e-02 6.401e-01 1.021e-03 1.143e-02 6.401e-01