Quantum hydrodynamics with trajectories: The nonlinear conservation form mixed/discontinuous Galerkin method with applications in chemistry

Authors:
C. Michoski;J. A. Evans;P. G. Schmitz;A. Vasseur
Affiliations:
Department of Chemistry and Biochemistry, University of Texas, Austin, TX 78712, United States;Institute for Computational Engineering and Sciences, University of Texas, Austin, TX 78712, United States;Department of Mathematics, University of Texas, Austin, TX 78712, United States;Department of Mathematics, University of Texas, Austin, TX 78712, United States
Venue:
Journal of Computational Physics
Year:
2009

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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.