The CICSAM (Compressive Interface Capturing Scheme for Arbitrary Meshes) method was implemented in the DLR TAU code to improve the advection of the VOF (Volume-Of-Fluid) values on both structured and unstructured grids. Two varying test scenarios are chosen to investigate the performance of the method. In the first test case, a sphere is transported along the edges of a rectangle. After one complete cycle, the final VOF distribution would analytically and visually be congruent with the initial distribution, thus, easing the evaluation of results. The computations were performed with a varying k-value and the results for k=0.5, 1.0 and 1.5 are presented. The k-value is introduced in the original CICSAM method as a weighting factor to control the dominance of the two different schemes for the calculation of the normalized face value, the ULTIME-QUICKEST and CBC. The best result on the unstructured grid was achieved with k=1.5. The result for k=1.0 showed the trend to converge to an octahedron. The interface and the spherical shape were preserved and remained within two grid cells. On the unstructured grid the sphere converged to a hexagon and lost its spherical shape. It was not possible to improve the result with varying k. The results showed a strong dependence on grid alignment, although the interface experienced no blurring when transported from fine to coarse grid discretization and vice versa. The second test case is the advection of an initial square VOF distribution through an oblique velocity field, i.e. 45deg flow. Very satisfying results with few discrepancies are again achieved on the structured grid. A similar behaviour as mentioned before is examined on the unstructured grid. The upper edge of the square deviated slightly from a straight line to a sine-like curve. On both grids, the lower left corner showed a slight tail-like blurring in flow direction. The CICSAM method proved to be a simple, easy to implement method with few algebraic operations. It showed very good results on structured grids in the frame of the chosen test cases. It is aimed to improve the results on unstructured grids with a dynamic adaptation where the VOF gradient is serving as the adaptation criterion.