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High-Order Simulation of Non-Linear Oscillations and Shocks in the Solar AtmosphereThe solar atmosphere presents a rich source of highly non-linear magneto-hydrodynamic phenomena: strong gradients and forcing terms result in both large shocks and oscillations. The additional requirements of energy balance and initialization in hydrostatic equilibrium compound the challenge of this problem. A wealth of observational data allows us to check the results of our simulations. The problem of simulating the solar atmosphere provides, in addition to an interesting system in its own right, a challenging testbed for high-order shock-capturing methods. We discuss the challenge of simulating solar atmospheric phenomena, concentrating on various high-order central methods ranging from second to fourth order. Our method is based on the central-upwind scheme of Kurganov, Noelle and Petrova, which we extend to high order via various interpolants. We investigate various initial data for our simulations, corresponding to observed conditions in different regions of the solar surface: the normal quiet sun and sunspots. When non-oscillatory using second- and third-order methods, we are able to reproduce non-trivial observational results. In particular we find a correlation between initial data and both the shock speeds and particle oscillation spectra that match observations in the corresponding regions. When using fourth-order WENO interpolants, we find that while the individual shock profiles at any given time appear non-oscillatory, spurious oscillations appear in the fields after long time integrations. The issue of initialization in hydrostatic equilibrium raises difficult issues. Careful treatment of the gravitational source term can reduce violations of hydrostatic equilibrium, but difficulties remain, primarily due to discontinuities in the piecewise-polynomial reconstructions. In the case of the Euler equations in gravity, the use of high-order methods reduces the violation of hydrostatic equilibrium to a sufficiently low level for the above described results to be obtained. Including various energy flux terms in the equations, however, leads to severe instability when hydrostatic balance is violated. We discuss various strategies to address this problem, including adaptive grid methods.
Document ID
20040068151
Acquisition Source
Ames Research Center
Document Type
Conference Paper
Authors
Bryson, S.
(NASA Ames Research Center Moffett Field, CA, United States)
Kosovichev, A.
(Stanford Univ. Stanford, CA, United States)
Levy, D.
(Stanford Univ. Stanford, CA, United States)
Date Acquired
August 21, 2013
Publication Date
January 1, 2004
Subject Category
Astrophysics
Meeting Information
Meeting: Presenation at the International Conference on Spectral and High-Order Methods
Location: Providence, RI
Country: United States
Start Date: June 21, 2004
End Date: June 25, 2004
Funding Number(s)
OTHER: 704-40-42
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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