Variational integrators for incompressible fluid flow, magnetohydrodynamics, complex fluid flow, and geophysical fluid dynamics

Evan Gawlik, Stanford University

This poster will present a family of variational integrators for incompressible fluid flow, magnetohydrodynamics, complex fluid flow, and geophysical fluid dynamics. A central role in our discretization of these systems is played by the geometric formulation of fluid dynamics, which views solutions to the governing equations for perfect fluid flow as geodesics on the group of volume-preserving diffeomorphisms of the fluid domain. By mimicking this framework at the discrete level, one obtains integrators that exhibit exact preservation of momenta arising from symmetries, automatic satisfaction of solenoidal constraints on vector fields, good long-term energy behavior, robustness with respect to the spatial and temporal resolution of the discretization, and applicability to irregular meshes.

Abstract Author(s): Evan Gawlik