Geometric variational finite element discretization of compressible fluids

Abstract: We review recent progress made in the development of structure preserving finite element integrators for compressible fluids. This approach combines the geometric formulation of fluid dynamics on groups of diffeomorphisms with finite element discretization techniques. A specific feature of the discrete geometric formulation is the occurrence of a nonholonomic right-invariant distribution on the discrete group of diffeomorphisms, that is shown to be isomorphic to a Raviart-Thomas finite element space. The resulting finite element discretizations correspond to weak forms of the compressible fluid equations that don't seem to have been used in the finite element literature. It extends previous work done on incompressible flows and at the lowest order on compressible fluids. We illustrate the benefits of this geometric approach and present potential future directions. This is a joint work with E. Gawlik.

MathematicsPhysics

Audience: researchers in the topic

Geometry, Dynamics and Mechanics Seminar

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