论文信息 - Velicity methods: Lagrangian numerical methods which preserve the Hamiltonian structure of incompres

Velicity methods: Lagrangian numerical methods which preserve the Hamiltonian structure of incompres

We present a Lagrangian numerical method valid in any space dimension for approximating solutions to the Incompressible Euler Equation. The method is based on the canonical Hamiltonian formulation of incompressible flow. The method preserves at least three invariants of the flow: the kinetic energy, the impulse, and the angular momentum. We present numerical results which validate the method and elucidate the structure of the Hamiltonian variables in two and three dimensions.

Tomas F. Buttke | T. F. Buttke

[1] A. Majda,et al. Vortex methods. II. Higher order accuracy in two and three dimensions , 1982 .

[2] J. Marsden,et al. A mathematical introduction to fluid mechanics , 1979 .

[3] V I Oseledets. COMMUNICATIONS OF THE MOSCOW MATHEMATICAL SOCIETY: On a new way of writing the Navier-Stokes equation. The Hamiltonian formalism , 1989 .

[4] Ole Hald,et al. Convergence of vortex methods for Euler’s equations , 1978 .

[5] J. W. Humberston. Classical mechanics , 1980, Nature.

[6] J. Munkres,et al. Calculus on Manifolds , 1965 .

[7] Ole H. Hald,et al. Convergence of Vortex methods for Euler's equations, III , 1987 .

[8] The evolution of a turbulent vortex , 1982 .

[9] A. Chorin. Numerical study of slightly viscous flow , 1973, Journal of Fluid Mechanics.

[10] Leslie Greengard,et al. A fast algorithm for particle simulations , 1987 .

[11] Paul H. Roberts,et al. A Hamiltonian theory for weakly interacting vortices , 1972 .

[12] D. A. Dunnett. Classical Electrodynamics , 2020, Nature.

[13] Christopher R. Anderson,et al. On Vortex Methods , 1985 .