The numerical simulation of interfacial and free surface flows is a vast and interesting topic in the areas of engineering and fundamental physics, such as the study of liquid-gas interfaces, formation of droplets, bubbles and sprays, combustion problems with liquid and gas reagents, study of wave motion and others. Many different methods for interface tracking exist, but Volume-of-Fluid and Level-Set methods are two of the most important. The Volume-of-Fluid preserves mass in a natural way but requires large computational resources. On the other hand, the Level-Set is not as accurate and mass conservative as the Volume-of-Fluid but is a faster way to track interfaces, representing them by the middle contour of a signed distance function. The objective of this work is to analyze the advantatges and drawbacks of the Volume-of-Fluid and Level-Set methods by solving the incompressible two-liquid Richtmyer-Meshkov instability and to compare the results to experimental data.

Peer Reviewed