Improved conservative level set method for free surface flow simulation

By coupling the standard and the conservative level set methods, an improved conservative level set method is proposed to capture the free surface smoothly with excellent mass conservation properties. The improvement lies in the fact that the surface normal is computed from a signed distance function instead of the Heaviside function. Comparing with the conservative level set method, the inevitable numerical discretization errors to point the surface normal in arbitrary directions could be eliminated, and the instability of the numerical solution could be improved efficiently. The advantage is clear in the straightforward combination of the standard level set and the conservative level set and a little effort is taken in coding compared with other coupled methods. The present method is validated with several well-known benchmark problems, including the 2-D Zalesak's disk rotating, the 3-D sphere stretching in deformation vortex and the dam break flow simulation. The results are shown to be in good agreement with the published experimental data and numerical results.