fluids cohomology

Cohomology in fluids

Prof.Albert Chern

Mar 13, 11:15 - 12:15

B4 L5 R5209

fluids cohomology fluid dynamics Geometry geometry processing

We present a topological analysis of the vorticity formulation in describing fluid dynamics. Despite its widespread use in fluid mechanics, this formulation is insufficient at describing fluid dynamics on a non-simply-connected domain. What is missing is an equation of motion for fluid's cohomology component, which exhibits fascinating dynamics previously under explored. Using geometric language, we derive the new equation of motion and establish new conservation laws, as Casimir invariants in Hamiltonian mechanics, for fluids on domains with general topology. Significantly, we present the first physically correct vortex method on curved surfaces with genus and boundaries.