1,541 research outputs found
Penalization for non-linear hyperbolic system
This paper proposes a volumetric penalty method to simulate the boundary
conditions for a non-linear hyperbolic problem. The boundary conditions are
assumed to be maximally strictly dissipative on a non-characteristic boundary.
This penalization appears to be quite natural since, after a natural change of
variable, the penalty matrix is an orthogonal projector. We prove the
convergence towards the solution of the wished hyperbolic problem and that this
convergence is sharp in the sense that it does not generate any boundary layer,
at any order. The proof involves an approximation by asymptotic expansion and
energy estimates in anisotropic Sobolev spaces
An improved method for solving quasilinear convection diffusion problems on a coarse mesh
A method is developed for solving quasilinear convection diffusion problems
starting on a coarse mesh where the data and solution-dependent coefficients
are unresolved, the problem is unstable and approximation properties do not
hold. The Newton-like iterations of the solver are based on the framework of
regularized pseudo-transient continuation where the proposed time integrator is
a variation on the Newmark strategy, designed to introduce controllable
numerical dissipation and to reduce the fluctuation between the iterates in the
coarse mesh regime where the data is rough and the linearized problems are
badly conditioned and possibly indefinite. An algorithm and updated marking
strategy is presented to produce a stable sequence of iterates as boundary and
internal layers in the data are captured by adaptive mesh partitioning. The
method is suitable for use in an adaptive framework making use of local error
indicators to determine mesh refinement and targeted regularization. Derivation
and q-linear local convergence of the method is established, and numerical
examples demonstrate the theory including the predicted rate of convergence of
the iterations.Comment: 21 pages, 8 figures, 1 tabl
Large time behavior and asymptotic stability of the two-dimensional Euler and linearized Euler equations
We study the asymptotic behavior and the asymptotic stability of the
two-dimensional Euler equations and of the two-dimensional linearized Euler
equations close to parallel flows. We focus on spectrally stable jet profiles
with stationary streamlines such that , a case that
has not been studied previously. We describe a new dynamical phenomenon: the
depletion of the vorticity at the stationary streamlines. An unexpected
consequence, is that the velocity decays for large times with power laws,
similarly to what happens in the case of the Orr mechanism for base flows
without stationary streamlines. The asymptotic behaviors of velocity and the
asymptotic profiles of vorticity are theoretically predicted and compared with
direct numerical simulations. We argue on the asymptotic stability of these
flow velocities even in the absence of any dissipative mechanisms.Comment: To be published in Physica D, nonlinear phenomena (accepted January
2010
Heat and mass transfer at a general three- dimensional stagnation point
Simultaneous effects of heat and mass transfer on boundary layer properties at three-dimensional stagnation point flow
Prominence Activation by Coronal Fast Mode Shock
An X5.4 class flare occurred in active region (AR) NOAA11429 on 2012 March 7.
The flare was associated with very fast coronal mass ejection (CME) with its
velocity of over 2500 km/s. In the images taken with STEREO-B/COR1, a dome-like
disturbance was seen to detach from expanding CME bubble and propagated
further. A Type-II radio burst was also observed at the same time. On the other
hand, in EUV images obtained by SDO/AIA, expanding dome-like structure and its
foot print propagating to the north were observed. The foot print propagated
with its average speed of about 670 km/s and hit a prominence located at the
north pole and activated it. While the activation, the prominence was strongly
brightened. On the basis of some observational evidence, we concluded that the
foot print in AIA images and the ones in COR1 images are the same, that is MHD
fast mode shock front. With the help of a linear theory, the fast mode mach
number of the coronal shock is estimated to be between 1.11 and 1.29 using the
initial velocity of the activated prominence. Also, the plasma compression
ratio of the shock is enhanced to be between 1.18 and 2.11 in the prominence
material, which we consider to be the reason of the strong brightening of the
activated prominence. The applicability of linear theory to the shock problem
is tested with nonlinear MHD simulation
Characteristic Evolution and Matching
I review the development of numerical evolution codes for general relativity
based upon the characteristic initial value problem. Progress in characteristic
evolution is traced from the early stage of 1D feasibility studies to 2D
axisymmetric codes that accurately simulate the oscillations and gravitational
collapse of relativistic stars and to current 3D codes that provide pieces of a
binary black hole spacetime. Cauchy codes have now been successful at
simulating all aspects of the binary black hole problem inside an artificially
constructed outer boundary. A prime application of characteristic evolution is
to extend such simulations to null infinity where the waveform from the binary
inspiral and merger can be unambiguously computed. This has now been
accomplished by Cauchy-characteristic extraction, where data for the
characteristic evolution is supplied by Cauchy data on an extraction worldtube
inside the artificial outer boundary. The ultimate application of
characteristic evolution is to eliminate the role of this outer boundary by
constructing a global solution via Cauchy-characteristic matching. Progress in
this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note:
updated version of arXiv:gr-qc/050809
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