skip to main content

Explore Research Products in the NSF-PAR

Title: Numerical efficacy study of data assimilation for the 2D magnetohydrodynamic equations
We study the computational efficiency of several nudging data assimilation algorithms for the 2D magnetohydrodynamic equations, using varying amounts and types of data. We find that the algorithms work with much less resolution in the data than required by the rigorous estimates in [7]. We also test other abridged nudging algorithms to which the analytic techniques in [7] do not seem to apply. These latter tests indicate, in particular, that velocity data alone is sufficient for synchronization with a chaotic reference solution, while magnetic data alone is not. We demonstrate that a new nonlinear nudging algorithm, which is adaptive in both time and space, synchronizes at a super exponential rate. [7] A. Biswas, J. Hudson, A. Larios and Y. Pei, Continuous data assimilation for the 2D magnetohydrodynamic equations using one component of the velocity and magnetic fields, Asymptot. Anal., 108 (2018), 1-43.  more » « less
Award ID(s):
1818754
NSF-PAR ID:
10146236
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Journal of computational dynamics
Volume:
6
Issue:
1
ISSN:
2158-2491
Page Range / eLocation ID:
131-145
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ( , Quarterly Journal of the Royal Meteorological Society)
    Abstract

    We develop and compare model‐error representation schemes derived from data assimilation increments and nudging tendencies in multidecadal simulations of the Community Atmosphere Model, version 6. Each scheme applies a bias correction during simulation runtime to the zonal and meridional winds. We quantify the extent to which such online adjustment schemes improve the model climatology and variability on daily to seasonal timescales. Generally, we observe about a 30% improvement to annual upper‐level zonal winds, with largest improvements in boreal spring (around 35%) and winter (around 47%). Despite only adjusting the wind fields, we additionally observe around 20% improvement to annual precipitation over land, with the largest improvements in boreal fall (around 36%) and winter (around 25%), and around 50% improvement to annual sea‐level pressure, globally. With mean‐state adjustments alone, the dominant pattern of boreal low‐frequency variability over the Atlantic (the North Atlantic Oscillation) is significantly improved. Additional stochasticity increases the modal explained variances further, which brings the variability closer to the observed value. A streamfunction tendency decomposition reveals that the improvement is due to an adjustment to the high‐ and low‐frequency eddy–eddy interaction terms. In the Pacific, the mean‐state adjustment alone led to an erroneous deepening of the Aleutian low, but this was remedied with the addition of stochastically selected tendencies. Finally, from a practical standpoint, we discuss the performance of using data assimilation increments versus nudging tendencies for an online model‐error representation.

     
    more » « less
  2. ; ( , Numerical Methods for Partial Differential Equations)
    Abstract

    We introduce, analyze, and test an interpolation operator designed for use with continuous data assimilation (DA) of evolution equations that are discretized spatially with the finite element method. The interpolant is constructed as an approximation of theL2projection operator onto piecewise constant functions on a coarse mesh, but which allows nudging to be done completely at the linear algebraic level, independent of the rest of the discretization, with a diagonal matrix that is simple to construct; it can even completely remove the need for explicit construction of a coarse mesh. We prove the interpolation operator has sufficient stability and accuracy properties, and we apply it to algorithms for both fluid transport DA and incompressible Navier–Stokes DA. For both applications we prove the DA solutions with arbitrary initial conditions converge to the true solution (up to discretization error) exponentially fast in time, and are thus long‐time accurate. Results of several numerical tests are given, which both illustrate the theory and demonstrate its usefulness on practical problems.

     
    more » « less
  3. ; ; ; ; ; ( , Frontiers in Astronomy and Space Sciences)
    Magnetic reconnection is the key mechanism for energy release in solar eruptions, where the high-temperature emission is the primary diagnostic for investigating the plasma properties during the reconnection process. Non-thermal broadening of high-temperature lines has been observed in both the reconnection current sheet (CS) and flare loop-top regions by UV spectrometers, but its origin remains unclear. In this work, we use a recently developed three-dimensional magnetohydrodynamic (MHD) simulation to model magnetic reconnection in the standard solar flare geometry and reveal highly dynamic plasma flows in the reconnection regions. We calculate the synthetic profiles of the Fe XXI 1354 Å line observed by the Interface Region Imaging Spectrograph (IRIS) spacecraft by using parameters of the MHD model, including plasma density, temperature, and velocity. Our model shows that the turbulent bulk plasma flows in the CS and flare loop-top regions are responsible for the non-thermal broadening of the Fe XXI emission line. The modeled non-thermal velocity ranges from tens of km s −1 to more than two hundred km s −1 , which is consistent with the IRIS observations. Simulated 2D spectral line maps around the reconnection region also reveal highly dynamic downwflow structures where the high non-thermal velocity is large, which is consistent with the observations as well. 
    more » « less
  4. ; ; ( , The Astrophysical Journal)
    Abstract

    The transport of waves and turbulence beyond the photosphere is central to the coronal heating problem. Turbulence in the quiet solar corona has been modeled on the basis of the nearly incompressible magnetohydrodynamic (NI MHD) theory to describe the transport of low-frequency turbulence in open magnetic field regions. It describes the evolution of the coupled majority quasi-2D and minority slab component, driven by the magnetic carpet and advected by a subsonic, sub-Alfvénic flow from the lower corona. In this paper, we couple the NI MHD turbulence transport model with an MHD model of the solar corona to study the heating problem in a coronal loop. In a realistic benchmark coronal loop problem, we find that a loop can be heated to ∼1.5 million K by transport and dissipation of MHD turbulence described by the NI MHD model. We also find that the majority 2D component is as important as the minority slab component in the heating of the coronal loop. We compare our coupled MHD/NI MHD model results with a reduced MHD (RMHD) model. An important distinction between these models is that RMHD solves for small-scale velocity and magnetic field fluctuations and obtains the actual viscous/resistive dissipation associated with their evolution whereas NI MHD evolves scalar moments of the fluctuating velocity and magnetic fields and approximates dissipation using an MHD turbulence phenomenology. Despite the basic differences between the models, their simulation results match remarkably well, yielding almost identical heating rates inside the corona.

     
    more » « less
  5. ; ; ; ; ; ; ; ; ; ( , The Astrophysical Journal)
    Abstract Nearly incompressible magnetohydrodynamic (NI MHD) theory for β ∼ 1 (or β ≪ 1) plasma has been developed and applied to the study of solar wind turbulence. The leading-order term in β ∼ 1 or β ≪ 1 plasma describes the majority of 2D turbulence, while the higher-order term describes the minority of slab turbulence. Here, we develop new NI MHD turbulence transport model equations in the high plasma beta regime. The leading-order term in a β ≫ 1 plasma is fully incompressible and admits both structures (flux ropes or magnetic islands) and slab (Alfvén waves) fluctuations. This paper couples the NI MHD turbulence transport equations with three fluid (proton, electron, and pickup ion) equations, and solves the 1D steady-state equations from 1–75 au. The model is tested against 27 yr of Voyager 2 data, and Ulysses and NH SWAP data. The results agree remarkably well, with some scatter, about the theoretical predictions. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email