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Fluid Dynamics Seminar
Mon., Nov. 11, 2013,
2:30 PM
Cullimore, Room 611
New Jersey Institute of Technology
Jet Schemes and Gradient-Augmented Level Set Methods
Benjamin Seibold
Department of Mathematics, Temple University
Abstract
Jet schemes are semi-Lagrangian advection approaches that evolve parts of the jet of the solution (i.e., function values and higher derivatives) along characteristic curves. Suitable Hermite interpolations give rise to methods that are high order accurate, yet optimally local, i.e., the update for the data at any grid point uses information from a single grid cell only. Jet schemes can be systematically derived from an evolve-and-project methodology in function spaces, which in particular yields stability estimates. We present a comparison of the accuracy and computational cost of jet schemes with WENO and Discontinuous Galerkin schemes. For interface evolution problems, jet schemes give rise to gradient-augmented level set methods (GALSM). These possess sub-grid resolution and yield accurate curvature approximations. We demonstrate how the GALSM's sub-grid resolution can serve to benefit two-phase fluid flow simulations, and how its optimal locality gives rise to a straightforward combination with adaptive mesh refinement (AMR).