  Gravitational waves from neutron-star and black-hole binaries carry valuable
information on their physical properties and probe physics inaccessible to the
laboratory. Although development of black-hole gravitational-wave templates in
the past decade has been revolutionary, the corresponding work for double
neutron-star systems has lagged. Neutron stars can be well-modelled as simple
barotropic fluids during the part of binary inspiral most relevant to
gravitational wave astronomy, but the crucial geometric and mathematical
consequences of this simplification have remained computationally unexploited.
In particular, Carter and Lichnerowicz have described barotropic fluid motion
via classical variational principles as conformally geodesic. Moreover,
Kelvin's circulation theorem implies that initially irrotational flows remain
irrotational. Applied to numerical relativity, these concepts lead to novel
Hamiltonian or Hamilton-Jacobi schemes for evolving relativistic fluid flows.
Hamiltonian methods can conserve not only flux, but also circulation and
symplecticity, and moreover do not require addition of an artificial atmosphere
typically required by standard conservative methods. These properties can allow
production of high-precision gravitational waveforms at low computational cost.
This canonical hydrodynamics approach is applicable to a wide class of problems
involving theoretical or computational fluid dynamics.
