Second-order accurate computation of curvatures in a level set framework using novel high-order reinitialization schemes

We present a high-order accurate scheme for the reinitialization equation of Sussman et al.(J. Comput. Phys. 114:146-159, [1994]) that guarantees accurate computation of the interface's curvatures in the context of level set methods. This scheme is an extension of the work of Russo and Smereka (J. Comput. Phys. 163:51-67, [2000]). We present numerical results in two and three spatial dimensions to demonstrate fourth-order accuracy for the reinitialized level set function, third-order accuracy for the normals and second-order accuracy for the interface's mean curvature in the L(1)- and L(infinity)-norms. We also exploit the work of Min and Gibou (UCLA CAM Report (06-22), [2006]) to show second-order accurate scheme for the computation of the mean curvature on non-graded adaptive grids.