Postprocessing of Non-Conservative Flux for Compatibility with Transport in Heterogeneous Media

A conservative flux postprocessing algorithm is presented for both steady-state and dynamic flow models. The postprocessed flux is shown to have the same convergence order as the original flux. An arbitrary flux approximation is projected into a conservative subspace by adding a piecewise constant correction that is minimized in a weighted $L^2$ norm. The application of a weighted norm appears to yield better results for heterogeneous media than the standard $L^2$ norm which has been considered in earlier works. We also study the effect of different flux calculations on the domain boundary. In particular we consider the continuous Galerkin finite element method for solving Darcy flow and couple it with a discontinuous Galerkin finite element method for an advective transport problem.Comment: 34 pages, 17 figures, 11 table

Spitzer 3.6 micron and 4.5 micron full-orbit lightcurves of WASP-18

We present new lightcurves of the massive hot Jupiter system WASP-18 obtained with the Spitzer spacecraft covering the entire orbit at 3.6 micron and 4.5 micron. These lightcurves are used to measure the amplitude, shape and phase of the thermal phase effect for WASP-18b. We find that our results for the thermal phase effect are limited to an accuracy of about 0.01% by systematic noise sources of unknown origin. At this level of accuracy we find that the thermal phase effect has a peak-to-peak amplitude approximately equal to the secondary eclipse depth, has a sinusoidal shape and that the maximum brightness occurs at the same phase as mid-occultation to within about 5 degrees at 3.6 micron and to within about 10 degrees at 4.5 micron. The shape and amplitude of the thermal phase curve imply very low levels of heat redistribution within the atmosphere of the planet. We also perform a separate analysis to determine the system geometry by fitting a lightcurve model to the data covering the occultation and the transit. The secondary eclipse depths we measure at 3.6 micron and 4.5 micron are in good agreement with previous measurements and imply a very low albedo for WASP-18b. The parameters of the system (masses, radii, etc.) derived from our analysis are in also good agreement with those from previous studies, but with improved precision. We use new high-resolution imaging and published limits on the rate of change of the mean radial velocity to check for the presence of any faint companion stars that may affect our results. We find that there is unlikely to be any significant contribution to the flux at Spitzer wavelengths from a stellar companion to WASP-18. We find that there is no evidence for variations in the times of eclipse from a linear ephemeris greater than about 100 seconds over 3 years.Comment: 17 pages, 10 figures. Accpeted for publication in MNRA

Multigrid for structures analysis

In structural dynamics the equations are usually expressed as finite elements. Neighbor elements need not be connected. The process of condensing a fine model into a coarse model and interpolating the low-frequency solution to the fine model is studied

Three-dimensional multigrid algorithms for the flux-split Euler equations

The Full Approximation Scheme (FAS) multigrid method is applied to several implicit flux-split algorithms for solving the three-dimensional Euler equations in a body fitted coordinate system. Each of the splitting algorithms uses a variation of approximate factorization and is implemented in a finite volume formulation. The algorithms are all vectorizable with little or no scalar computation required. The flux vectors are split into upwind components using both the splittings of Steger-Warming and Van Leer. The stability and smoothing rate of each of the schemes are examined using a Fourier analysis of the complete system of equations. Results are presented for three-dimensional subsonic, transonic, and supersonic flows which demonstrate substantially improved convergence rates with the multigrid algorithm. The influence of using both a V-cycle and a W-cycle on the convergence is examined

Viscous compressible flow direct and inverse computation and illustrations

An algorithm for laminar and turbulent viscous compressible two dimensional flows is presented. For the application of precise boundary conditions over an arbitrary body surface, a body-fitted coordinate system is used in the physical plane. A thin-layer approximation of tne Navier-Stokes equations is introduced to keep the viscous terms relatively simple. The flow field computation is performed in the transformed plane. A factorized, implicit scheme is used to facilitate the computation. Sample calculations, for Couette flow, developing pipe flow, an isolated airflow, two dimensional compressor cascade flow, and segmental compressor blade design are presented. To a certain extent, the effective use of the direct solver depends on the user's skill in setting up the gridwork, the time step size and the choice of the artificial viscosity. The design feature of the algorithm, an iterative scheme to correct geometry for a specified surface pressure distribution, works well for subsonic flows. A more elaborate correction scheme is required in treating transonic flows where local shock waves may be involved

Microlensing with advanced contour integration algorithm: Green's theorem to third order, error control, optimal sampling and limb darkening

Microlensing light curves are typically computed either by ray-shooting maps or by contour integration via Green's theorem. We present an improved version of the second method that includes a parabolic correction in Green's line integral. In addition, we present an accurate analytical estimate of the residual errors, which allows the implementation of an optimal strategy for the contour sampling. Finally, we give a prescription for dealing with limb-darkened sources reaching arbitrary accuracy. These optimizations lead to a substantial speed-up of contour integration codes along with a full mastery of the errors.Comment: 34 pages, 11 figure