1,122 research outputs found

    The NASA Ames Research Center one- and two-dimensional stratospheric models. Part 2: The two-dimensional model

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    The two-dimensional model of stratospheric constituents is presented in detail. The derivation of pertinent transport parameters and the numerical solution of the species continuity equations, including a technique for treating the stiff differential equations that represent the chemical kinetic terms, and appropriate methods for simulating the diurnal variations of the solar zenith angle and species concentrations are discussed. Predicted distributions of tracer constituents (ozone, carbon 14, nitric acid) are compared with observed distributions

    Moment-Based Accelerators for Kinetic Problems with Application to Inertial Confinement Fusion

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    In inertial confinement fusion (ICF), the kinetic ion and charge separation field effects may play a significant role in the difference between the measured neutron yield in experiments and the predicted yield from fluid codes. Two distinct of approaches exists in modeling plasma physics phenomena: fluid and kinetic approaches. While the fluid approach is computationally less expensive, robust closures are difficult to obtain for a wide separation in temperature and density. While the kinetic approach is a closed system, it resolves the full 6D phase space and classic explicit numerical schemes restrict both the spatial and time-step size to a point where the method becomes intractable. Classic implicit system require the storage and inversion of a very large linear system which also becomes intractable. This dissertation will develop a new implicit method based on an emerging moment-based accelerator which allows one to step over stiff kinetic time-scales. The new method converges the solution per time-step stably and efficiently compared to a standard Picard iteration. This new algorithm will be used to investigate mixing in Omega ICF fuel-pusher interface at early time of the implosion process, fully kinetically

    Explicit schemes for time propagating many-body wavefunctions

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    Accurate theoretical data on many time-dependent processes in atomic and molecular physics and in chemistry require the direct numerical solution of the time-dependent Schr\"odinger equation, thereby motivating the development of very efficient time propagators. These usually involve the solution of very large systems of first order differential equations that are characterized by a high degree of stiffness. We analyze and compare the performance of the explicit one-step algorithms of Fatunla and Arnoldi. Both algorithms have exactly the same stability function, therefore sharing the same stability properties that turn out to be optimum. Their respective accuracy however differs significantly and depends on the physical situation involved. In order to test this accuracy, we use a predictor-corrector scheme in which the predictor is either Fatunla's or Arnoldi's algorithm and the corrector, a fully implicit four-stage Radau IIA method of order 7. We consider two physical processes. The first one is the ionization of an atomic system by a short and intense electromagnetic pulse; the atomic systems include a one-dimensional Gaussian model potential as well as atomic hydrogen and helium, both in full dimensionality. The second process is the decoherence of two-electron quantum states when a time independent perturbation is applied to a planar two-electron quantum dot where both electrons are confined in an anharmonic potential. Even though the Hamiltonian of this system is time independent the corresponding differential equation shows a striking stiffness. For the one-dimensional Gaussian potential we discuss in detail the possibility of monitoring the time step for both explicit algorithms. In the other physical situations that are much more demanding in term of computations, we show that the accuracy of both algorithms depends strongly on the degree of stiffness of the problem.Comment: 24 pages, 14 Figure

    How AD Can Help Solve Differential-Algebraic Equations

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    A characteristic feature of differential-algebraic equations is that one needs to find derivatives of some of their equations with respect to time, as part of so called index reduction or regularisation, to prepare them for numerical solution. This is often done with the help of a computer algebra system. We show in two significant cases that it can be done efficiently by pure algorithmic differentiation. The first is the Dummy Derivatives method, here we give a mainly theoretical description, with tutorial examples. The second is the solution of a mechanical system directly from its Lagrangian formulation. Here we outline the theory and show several non-trivial examples of using the "Lagrangian facility" of the Nedialkov-Pryce initial-value solver DAETS, namely: a spring-mass-multipendulum system, a prescribed-trajectory control problem, and long-time integration of a model of the outer planets of the solar system, taken from the DETEST testing package for ODE solvers

    Symplectic-energy-momentum preserving variational integrators

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    The purpose of this paper is to develop variational integrators for conservative mechanical systems that are symplectic and energy and momentum conserving. To do this, a space–time view of variational integrators is employed and time step adaptation is used to impose the constraint of conservation of energy. Criteria for the solvability of the time steps and some numerical examples are given

    Time integration and steady-state continuation for 2d lubrication equations

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    Lubrication equations allow to describe many structurin processes of thin liquid films. We develop and apply numerical tools suitable for their analysis employing a dynamical systems approach. In particular, we present a time integration algorithm based on exponential propagation and an algorithm for steady-state continuation. In both algorithms a Cayley transform is employed to overcome numerical problems resulting from scale separation in space and time. An adaptive time-step allows to study the dynamics close to hetero- or homoclinic connections. The developed framework is employed on the one hand to analyse different phases of the dewetting of a liquid film on a horizontal homogeneous substrate. On the other hand, we consider the depinning of drops pinned by a wettability defect. Time-stepping and path-following are used in both cases to analyse steady-state solutions and their bifurcations as well as dynamic processes on short and long time-scales. Both examples are treated for two- and three-dimensional physical settings and prove that the developed algorithms are reliable and efficient for 1d and 2d lubrication equations, respectively.Comment: 33 pages, 16 figure

    Computational methods and software systems for dynamics and control of large space structures

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    Two key areas of crucial importance to the computer-based simulation of large space structures are discussed. The first area involves multibody dynamics (MBD) of flexible space structures, with applications directed to deployment, construction, and maneuvering. The second area deals with advanced software systems, with emphasis on parallel processing. The latest research thrust in the second area involves massively parallel computers
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