751 research outputs found
Adaptive time-stepping for incompressible flow part I: scalar advection-diffusion
Even the simplest advection-diffusion problems can exhibit multiple time scales. This means that robust variable step time integrators are a prerequisite if such problems are to be efficiently solved computationally. The performance of the second order trapezoid rule using an explicit Adams–Bashforth method for error control is assessed in this work. This combination is particularly well suited to long time integration of advection-dominated problems. Herein it is shown that a stabilized implementation of the trapezoid rule leads to a very effective integrator in other situations: specifically diffusion problems with rough initial data; and general advection-diffusion problems with different physical time scales governing the system evolution
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Adaptive time-stepping for incompressible flow. Part II: Navier-Stokes equations
We outline a new class of robust and efficient methods for solving the Navier- Stokes equations. We describe a general solution strategy that has two basic building blocks: an implicit time integrator using a stabilized trapezoid rule with an explicit Adams-Bashforth method for error control, and a robust Krylov subspace solver for the spatially discretized system. We present numerical experiments illustrating the potential of our approach. © 2010 Society for Industrial and Applied Mathematics
Revisiting the Rigidly Rotating Magnetosphere model for Ori E - II. Magnetic Doppler imaging, arbitrary field RRM, and light variability
The initial success of the Rigidly Rotating Magnetosphere (RRM) model
application to the B2Vp star sigma OriE by Townsend, Owocki & Groote (2005)
triggered a renewed era of observational monitoring of this archetypal object.
We utilize high-resolution spectropolarimetry and the magnetic Doppler imaging
(MDI) technique to simultaneously determine the magnetic configuration, which
is predominately dipolar, with a polar strength Bd = 7.3-7.8 kG and a smaller
non-axisymmetric quadrupolar contribution, as well as the surface distribution
of abundance of He, Fe, C, and Si. We describe a revised RRM model that now
accepts an arbitrary surface magnetic field configuration, with the field
topology from the MDI models used as input. The resulting synthetic Ha emission
and broadband photometric observations generally agree with observations,
however, several features are poorly fit. To explore the possibility of a
photospheric contribution to the observed photometric variability, the MDI
abundance maps were used to compute a synthetic photospheric light curve to
determine the effect of the surface inhomogeneities. Including the computed
photospheric brightness modulation fails to improve the agreement between the
observed and computed photometry. We conclude that the discrepancies cannot be
explained as an effect of inhomogeneous surface abundance. Analysis of the UV
light variability shows good agreement between observed variability and
computed light curves, supporting the accuracy of the photospheric light
variation calculation. We thus conclude that significant additional physics is
necessary for the RRM model to acceptably reproduce observations of not only
sigma Ori E, but also other similar stars with significant stellar
wind-magnetic field interactions.Comment: 16 pages, 17 figures, accepted for publication in MNRA
Double layer in ionic liquids: Overscreening vs. crowding
We develop a simple Landau-Ginzburg-type continuum theory of solvent-free
ionic liquids and use it to predict the structure of the electrical double
layer. The model captures overscreening from short-range correlations, dominant
at small voltages, and steric constraints of finite ion sizes, which prevail at
large voltages. Increasing the voltage gradually suppresses overscreening in
favor of the crowding of counterions in a condensed inner layer near the
electrode. The predicted ion profiles and capacitance-voltage relations are
consistent with recent computer simulations and experiments on room-temperature
ionic liquids, using a correlation length of order the ion size.Comment: 4 pages + supplementary informatio
Efficient Adaptive Stochastic Collocation Strategies for Advection-Diffusion Problems with Uncertain Inputs
Physical models with uncertain inputs are commonly represented as parametric
partial differential equations (PDEs). That is, PDEs with inputs that are
expressed as functions of parameters with an associated probability
distribution. Developing efficient and accurate solution strategies that
account for errors on the space, time and parameter domains simultaneously is
highly challenging. Indeed, it is well known that standard polynomial-based
approximations on the parameter domain can incur errors that grow in time. In
this work, we focus on advection-diffusion problems with parameter-dependent
wind fields. A novel adaptive solution strategy is proposed that allows users
to combine stochastic collocation on the parameter domain with off-the-shelf
adaptive timestepping algorithms with local error control. This is a
non-intrusive strategy that builds a polynomial-based surrogate that is adapted
sequentially in time. The algorithm is driven by a so-called hierarchical
estimator for the parametric error and balances this against an estimate for
the global timestepping error which is derived from a scaling argument.Comment: 29 pages, 14 figure
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