On controlling nonlinear dissipation in high order filter methods for ideal and non-ideal MHD

The newly developed adaptive numerical dissipation control in spatially high order filter schemes for the compressible Euler and Navier-Stokes equations has been recently extended to the ideal and non-ideal magnetohydrodynamics (MHD) equations. These filter schemes are applicable to complex unsteady MHD high-speed shock/shear/turbulence problems. They also provide a natural and efficient way for the minimization of Div(B) numerical error. The adaptive numerical dissipation mechanism consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and leave the rest of the region free from numerical dissipation contamination. The numerical dissipation considered consists of high order linear dissipation for the suppression of high frequency oscillation and the nonlinear dissipative portion of high-resolution shock-capturing methods for discontinuity capturing. The applicable nonlinear dissipative portion of high-resolution shock-capturing methods is very general. The objective of this paper is to investigate the performance of three commonly used types of nonlinear numerical dissipation for both the ideal and non-ideal MHD

Duality Symmetry in Kaluza-Klein n+D+dn+D+d Dimensional Cosmological Model

It is shown that, with the only exception of $n=2$, the Einstein-Hilbert action in $n+D+d$ dimensions, with $n$ times, is invariant under the duality transformation $a\to \frac{1}{a}$ and $b\to \frac{1}{b}$, where $a$ is a Friedmann-Robertson-Walker scale factor in $D$ dimensions and $b$ a Brans-Dicke scalar field in $d$ dimensions respectively. We investigate the $2+D+d$ dimensional cosmological model in some detail.Comment: 23 pages, Late

A Numerical Study of Resistivity and Hall Effects for a Compressible MHD Model

The effect of resistive, Hall, and viscous terms on the flow structure compared with compressible ideal MHD is studied numerically for a one-fluid non-ideal MHD model. The goal of the present study is to shed some light on the emerging area of non-ideal MHD modeling and simulation. Numerical experiments are performed on a hypersonic blunt body flow with future application to plasma aerodynamics flow control in reentry vehicles. Numerical experiments are also performed on a magnetized time-developing mixing layer with possible application to magnetic/turbulence mixing

Characterizing Long-Period Transiting Planets Observed by Kepler

Kepler will monitor a sufficient number of stars that it is likely to detect single transits of planets with periods longer than the mission lifetime. We show that by combining the exquisite Kepler photometry of such transits with precise radial velocity observations taken over a reasonable timescale (~ 6 months) after the transits, and assuming circular orbits, it is possible to estimate the periods of these transiting planets to better than 20%, for planets with radii greater than that of Neptune, and the masses to within a factor of 2, for planets with masses larger than or about equal to the mass of Jupiter. Using a Fisher matrix analysis, we derive analytic estimates for the uncertainties in the velocity of the planet and the acceleration of the star at the time of transit, which we then use to derive the uncertainties for the planet mass, radius, period, semimajor axis, and orbital inclination. Finally, we explore the impact of orbital eccentricity on the estimates of these quantities.Comment: 31 pages, 8 figures, Accepted to Ap

Variable high-order multiblock overlapping grid methods for mixed steady and unsteady multiscale viscous flows, part II: hypersonic nonequilibrium flows

The variable high-order multiblock overlapping (overset) grids method of Sjogreen & Yee (CiCP, Vol.5, 2008) for a perfect gas has been extended to nonequilibrium flows. This work makes use of the recently developed high-order well-balanced shock-capturing schemes and their filter counterparts (Wang et al., J. Comput. Phys., 2009, 2010) that exactly preserve certain non-trivial steady state solutions of the chemical nonequilibrium governing equations. Multiscale turbulence with strong shocks and flows containing both steady and unsteady components is best treated by mixing of numerical methods and switching on the appropriate scheme in the appropriate subdomains of the flow fields, even under the multiblock grid or adaptive grid refinement framework. While low dissipative sixth- or higher-order shock-capturing filter methods are appropriate for unsteady turbulence with shocklets, second- and third-order shock-capturing methods are more effective for strong steady or nearly steady shocks in terms of convergence. It is anticipated that our variable high-order overset grid framework capability with its highly modular design will allow an optimum synthesis of these new algorithms in such a way that the most appropriate spatial discretizations can be tailored for each particular region of the flow. In this paper some of the latest developments in single block high-order filter schemes for chemical nonequilibrium flows are applied to overset grid geometries. The numerical approach is validated on a number of test cases characterized by hypersonic conditions with strong shocks, including the reentry flow surrounding a 3D Apollo-like NASA Crew Exploration Vehicle that might contain mixed steady and unsteady components, depending on the flow conditions

Analytic Approximations for Transit Light Curve Observables, Uncertainties, and Covariances

The light curve of an exoplanetary transit can be used to estimate the planetary radius and other parameters of interest. Because accurate parameter estimation is a non-analytic and computationally intensive problem, it is often useful to have analytic approximations for the parameters as well as their uncertainties and covariances. Here we give such formulas, for the case of an exoplanet transiting a star with a uniform brightness distribution. We also assess the advantages of some relatively uncorrelated parameter sets for fitting actual data. When limb darkening is significant, our parameter sets are still useful, although our analytic formulas underpredict the covariances and uncertainties.Comment: 33 pages, 14 figure

LES of Temporally Evolving Mixing Layers by an Eighth-Order Filter Scheme

An eighth-order filter method for a wide range of compressible flow speeds (H.C. Yee and B. Sjogreen, Proceedings of ICOSAHOM09, June 22-26, 2009, Trondheim, Norway) are employed for large eddy simulations (LES) of temporally evolving mixing layers (TML) for different convective Mach numbers (Mc) and Reynolds numbers. The high order filter method is designed for accurate and efficient simulations of shock-free compressible turbulence, turbulence with shocklets and turbulence with strong shocks with minimum tuning of scheme parameters. The value of Mc considered is for the TML range from the quasi-incompressible regime to the highly compressible supersonic regime. The three main characteristics of compressible TML (the self similarity property, compressibility effects and the presence of large-scale structure with shocklets for high Mc) are considered for the LES study. The LES results using the same scheme parameters for all studied cases agree well with experimental results of Barone et al. (2006), and published direct numerical simulations (DNS) work of Rogers & Moser (1994) and Pantano & Sarkar (2002)