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fluids cohomology
Cohomology in fluids
Prof.Albert Chern
Mar 13, 11:15
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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.
