Event Detail

Event Type: 
Department Colloquium
Thursday, May 5, 2005 - 08:00
Covell 221

Speaker Info

Courant Institute of Mathematical Sciences, New York University

A variety of physical phenomena in traditional fluid mechanics, groundwater flow, meteorology and other areas can be described by hyperbolic conservation laws. Hyperbolic equations have a deceptively simple structure but solving them accurately and efficiently is a challenge. The property common to hyperbolic problems, and indeed the main difficulty when dealing with them both analytically and numerically, is the appearance of discontinuities, such as shock waves and contact discontinuities, even with smooth initial data. The discontinuous Galerkin method (DGM) provides an appealing approach for addressing such problems. The solution space is discontinuous relative to a structured or unstructured mesh and this allows solution discontinuities to be captured sharply relative to the computational mesh. A polynomial basis helps in achieving arbitrary higher-order accuracy in smooth regions. Adaptive mesh refinement is used to concentrate the computational effort in regions requiring greater resolution. The DGM simplifies adaptivity since inter-element continuity is required neither for h-refinement (mesh refinement and coarsening) nor for p-refinement (method order variation). We describe our approach to computing higher-order accurate solutions for time dependent fluid flows in complex geometries on structured and unstructured meshes. We review several aspects of our work including basis construction, solution limiting, adaptivity, and accurate representations of boundary conditions. Emphasis is put on efficiency and robustness.