Hamiltonian differencing of fluid dynamics

By analyzing the Hamiltonian structures of several representations of continuous Lagrangian fluid dynamics, a universal Hamiltonian form is developed which unifies those structures and applies both to the continuous and spatially discrete cases. Then the universal Hamiltonian form is used as a “template” for generating numerical differencing schemes which retain the underlying Hamiltonian structure of the continuous theory. Examples are discussed of these spatial differencing schemes for the Euler equations in one, two, and three dimensions. In one dimension, the nondissipative part of the von Neumann-Richtmeyer scheme is recovered as a special case.