Hamiltonian particle hydrodynamics

Abstract

Particle-based hydrodynamics models offer distinct advantages over Eulerian and Lagrangian hydrocodes in particular shock physics applications. Particle models are designed to avoid the mesh distortion and state variable diffusion problems which can hinder the effective use of Lagrangian and Eulerian codes, respectively. However, existing particle-in-cell and smooth particle hydrodynamics methods employ particles which are actually moving interpolation points. The latter distinction has been emphasized in the more recent development of element-free Galerkin theory. As a result, general formulations of all of the aforementioned methods are based on the partial differential equation forms of the continuum balance laws which underlie conventional Eulerian and Lagrangian schemes. An alternative modeling methodology, based on the application of Hamilton's equations to a system of deforming physical particles, provides a fully Lagrangian, energy-based approach to shock physics simulations. Neither interpolations of field variables nor continuum balance laws are used to establish the state equations for the particle system. Mechanical and thermal interaction of the particles is accounted for by nonholonomic constraints which determine both particle entropy evolution and particle collision loads. Application of the method is illustrated by simulation of a wall shock problem.