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

Journal Article · Thu Dec 10 00:00:00 EST 2009 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2009.08.011· OSTI ID:21333894

Evans, J A ^[1]; Schmitz, P G; Vasseur, A ^[2]

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1. Institute for Computational Engineering and Sciences, University of Texas, Austin, TX 78712 (United States)
2. Department of Mathematics, University of Texas, Austin, TX 78712 (United States)

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.

• OSTI ID: 21333894
• Journal Information: Journal of Computational Physics, Vol. 228, Issue 23; Other Information: DOI: 10.1016/j.jcp.2009.08.011; PII: S0021-9991(09)00448-3; Copyright (c) 2009 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY-VALUE PROBLEMS
CONSERVATION LAWS
FINITE ELEMENT METHOD
HYDRODYNAMICS
LAGRANGIAN FUNCTION
NONLINEAR PROBLEMS
SCALE INVARIANCE
SCHROEDINGER EQUATION
TIME DEPENDENCE
TUNNEL EFFECT