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Colloquium, Winter 2006

Day: Monday January 30 Time: 4:00pm Place: BH 428 Title:  High-order discontinuous Galerkin methods for nonlinear hyperbolic conservation laws. Speaker: Lilia Krovodonova Abstract:  A variety of physical phenomena in fluid mechanics, groundwater flow, meteorology and other areas can be described by hyperbolic conservation laws. The common property of hyperbolic problems and the main difficulty of dealing with them analytically and numerically is the appearance of discontinuities such as shock waves even with smooth initial data. High-order methods can be very efficient for such problems but they are difficult to construct since numerical solutions develop oscillations near discontinuities.     We describe our approach to computing high-order accurate solutions for time dependent fluid flows on structured and unstructured meshes. We review several aspects of our recent work including solution limiting, adaptivity, and the accurate imposition of boundary conditions.