Marker Re-Distancing (Mrd) Algorithm For High-Fidelity Interface Tracking On Arbitrary Meshes

A new sharp high-order interface tracking method for multi material flow problems on unstructured meshes is presented. This marker re-distancing (MRD) method is designed to work accurately and robustly on unstructured, generally highly distorted meshes, necessitated by applications within ALE-based hydrocodes. The method is a hybrid of a Lagrangian marker tracking method and a novel discontinuous Galerkin (DG) projection based level set re-distancing algorithm. The re-distancing method is formulated as a constrained minimization problem and is shown to obtain arbitrary orders of convergence for smooth interfaces. High-order (>2nd) re-distancing on irregular meshes is a must for applications were the interfacial curvature is important for the underlying physics, such as surface tension, wetting, and detonation shock dynamics. Since no PDE is solved for re-distancing, the method does not have a stability time step restriction, which is particularly useful in combination with AMR, used here to efficiently resolve fine interface features. In addition, the method can robustly handle discontinuities in the distance function without explicit utilization of solution limiters. Results will be shown for a number of different interface geometries, which will demonstrate the method's capability of obtaining high-fidelity results on arbitrary meshes.