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 methods. The kinematics of the interface is treated in a Lagrangian (FT) manner, by tracking markers placed 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 " anchoring " 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 discretization 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 ≈ 10 iterations (CFL ≈ 10 4), in contrast to the explicit redistancing which requires hundreds of iterations with CFL ≤ 1. 1. Motivation and background. The present study is motivated by the need for high-fidelity simulations of flows with significant interface curvature (surface tension) effects. These effects are important in multiphase flow applications, where the interfacial instabilities (of either Rayleigh–Taylor, Kelvin–Helmholtz, or Marangoni origin) are the driving mechanisms for the evolution of the interface topology, defining the physics of multifluid mixing, heat transfer, and phase change. There are also numerous curvature-effect-dominant applications in computational geometry, grid generation , image processing, computer vision, optimization, computer-aided design, etc. [36]. The applications of primary interest here are the physics of boiling multiphase flows in nuclear energy systems [21] and the atmospheric dissemination of chemical agents [22, 44]. There are three major and distinct interface tracking methods developed in the past 30 years: front tracking (FT) [4, 11], volume tracking (VT) [14, 33], and level set (LS) [27, 36]. Each method has its own pros and cons. FT algorithms are apparently the most accurate, but unfortunately their implementation is nontrivial (especially *