Computer Science NASC Seminar

Jet Schemes and Gradient-Augmented Level Set Methods

Benjamin Seibold, Temple University

February 01, 2013 10:00AM
Warren Weaver Hall, Room 1302
251 Mercer Street
New York, NY, 10012-1110

Spring 2013 NASC Seminars Calendar


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. The benefits
of this feature are demonstrated with a two-phase fluid flow
simulation. Moreover, we demonstrate how the optimal locality of jet
schemes gives rise to a straightforward combination with of adaptive
mesh refinement (AMR).

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