Quantum Hydrodynamics with Trajectories: The Nonlinear Conservation Form Mixed/Discontinuous Galerkin Method with Applications in Chemistry
arXiv:0904.3380 · doi:10.1016/j.jcp.2009.08.011
Abstract
We present a solution to the conservation form (Eulerian form) of the quantum hydrodynamic equations which arise in chemical dynamics by implementing a mixed/discontinuous Galerkin (MDG) finite element numerical scheme. We show that this methodology is stable, showing good accuracy and a remarkable scale invariance in its solution space. In addition the MDG method is robust, adapting well to various initial-boundary value problems of particular significance in a range of physical and chemical applications. We further show explicitly how to recover the Lagrangian frame (or pathline) solutions.
30 pages, 26 figures