Marker redistancing/level set method for high-fidelity implicit interface tracking

A hybrid of the front tracking (FT) and the level set (LS) methods is introduced, combining advantages and removing drawbacks of both metho ds. The kinematics of the interface is treated in a Lagrangian (FT) manner, by tracking markers p laced at the interface. The markers are not connected-instead, the interface topology is resolved in an Eulerian (LS) framework, by wrapping a signed distance function around Lagrangian markers each time the markers move. For accuracy and efficiency, we have developed a high-order "anchor i ng" algorithm and an implicit PDE- based redistancing. We have demonstrated that the method is 3rd-order accurate in space, near the markers, and therefore 1st-order convergent in curvature; this is in contrast to traditional PDE-based reinitialization algorithms, which tend to slightly relocate the zero level set and can be shown to be nonconvergent in curvature. The implicit pseudo-time discret ization of the redistancing equation is implemented within the Jacobian-free Newton-Krylov (JFNK) framework combined with ILU(k) preconditioning. Due to the LS localization, the bandwidth of the Jacobian matrix is nearly constant, and the ILU preconditioning scales as ̃ N log(√N) in two dimensions, which implies efficiency and good scalability of the overall algorithm. We have demonstrated that the steady-state solutions in pseudo-time can be achieved very efficiently, with a 10 iterations (CFL sy& 10⁴), in contrast to the explicit redistancing which requires hundreds of iterations with CFL ≤ 1.