Structure-preserving discretization of incompressible fluids

By Dmitry Pavlov, Patrick Mullen, Y. Tong, Eva Kanso, Jerrold E. Marsden, Mathieu Desbrun. 2009

141 citations recorded by the source corpus.

The geometric nature of Euler fluids has been clearly identified and extensively studied over the years, culminating with Lagrangian and Hamiltonian descriptions of fluid dynamics where the configuration space is defined as the volume-preserving diffeomorphisms, and Kelvin’s circulation theorem is viewed as a consequence of Noether’s theorem associated with the particle relabeling symmetry of fluid mechanics. However computational approaches to fluid mechanics have been largely derived from a numerical–analytic point of view, and are rarely designed with structure preservation in mind, and often suffer from spurious numerical artifacts such as energy and circulation drift. In contrast, this paper geometrically derives discrete equations of motion for fluid dynamics from first principles in a purely Eulerian form. Our approach approximates the group of volume-preserving diffeomorphisms using a finite-dimensional Lie group, and associated discrete Euler equations are derived from a variational principle with non-holonomic constraints. The resulting discrete equations of motion yield a structure-preserving time integrator with good long-term energy behavior and for which an exact discrete Kelvin’s circulation theorem holds.

Subfields: Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/5154ebfdffb3f565ce2832e03acd0afd7d85f0f6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

  1. Claudio Paniconi
  2. Mario Putti

Citations in the corpus