Topological characteristics of oil and gas reservoirs and their applications

We demonstrate applications of topological characteristics of oil and gas reservoirs considered as three-dimensional bodies to geological modeling.Comment: 12 page

Topological Mixing with Ghost Rods

Topological chaos relies on the periodic motion of obstacles in a two-dimensional flow in order to form nontrivial braids. This motion generates exponential stretching of material lines, and hence efficient mixing. Boyland et al. [P. L. Boyland, H. Aref, and M. A. Stremler, J. Fluid Mech. 403, 277 (2000)] have studied a specific periodic motion of rods that exhibits topological chaos in a viscous fluid. We show that it is possible to extend their work to cases where the motion of the stirring rods is topologically trivial by considering the dynamics of special periodic points that we call ghost rods, because they play a similar role to stirring rods. The ghost rods framework provides a new technique for quantifying chaos and gives insight into the mechanisms that produce chaos and mixing. Numerical simulations for Stokes flow support our results.Comment: 13 pages, 11 figures. RevTeX4 format. (Final version

A robust method for calculating interface curvature and normal vectors using an extracted local level set

The level-set method is a popular interface tracking method in two-phase flow simulations. An often-cited reason for using it is that the method naturally handles topological changes in the interface, e.g. merging drops, due to the implicit formulation. It is also said that the interface curvature and normal vectors are easily calculated. This last point is not, however, the case in the moments during a topological change, as several authors have already pointed out. Various methods have been employed to circumvent the problem. In this paper, we present a new such method which retains the implicit level-set representation of the surface and handles general interface configurations. It is demonstrated that the method extends easily to 3D. The method is validated on static interface configurations, and then applied to two-phase flow simulations where the method outperforms the standard method and the results agree well with experiments.Comment: 31 pages, 18 figure

The Semi Implicit Gradient Augmented Level Set Method

Here a semi-implicit formulation of the gradient augmented level set method is presented. By tracking both the level set and it's gradient accurate subgrid information is provided,leading to highly accurate descriptions of a moving interface. The result is a hybrid Lagrangian-Eulerian method that may be easily applied in two or three dimensions. The new approach allows for the investigation of interfaces evolving by mean curvature and by the intrinsic Laplacian of the curvature. In this work the algorithm, convergence and accuracy results are presented. Several numerical experiments in both two and three dimensions demonstrate the stability of the scheme.Comment: 19 Pages, 14 Figure

A weak acceleration effect due to residual gravity in a multiply connected universe

Could cosmic topology imply dark energy? We use a weak field (Newtonian) approximation of gravity and consider the gravitational effect from distant, multiple copies of a large, collapsed (virialised) object today (i.e. a massive galaxy cluster), taking into account the finite propagation speed of gravity, in a flat, multiply connected universe, and assume that due to a prior epoch of fast expansion (e.g. inflation), the gravitational effect of the distant copies is felt locally, from beyond the naively calculated horizon. We find that for a universe with a $T^1xR^2$ spatial section, the residual Newtonian gravitational force (to first order) provides an anisotropic effect that repels test particles from the cluster in the compact direction, in a way algebraically similar to that of dark energy. For a typical test object at comoving distance $\chi$ from the nearest dense nodes of the cosmic web of density perturbations, the pressure-to-density ratio $w$ of the equation of state in an FLRW universe, is w \sim - (\chi/L)^3, where $L$ is the size of the fundamental domain, i.e. of the universe. Clearly, |w|<<1. For a T^3 spatial section of exactly equal fundamental lengths, the effect cancels to zero. For a T^3 spatial section of unequal fundamental lengths, the acceleration effect is anisotropic in the sense that it will *tend to equalise the three fundamental lengths*. Provided that at least a modest amount of inflation occurred in the early Universe, and given some other conditions, multiple connectedness does generate an effect similar to that of dark energy, but the amplitude of the effect at the present epoch is too small to explain the observed dark energy density and its anisotropy makes it an unrealistic candidate for the observed dark energy.Comment: 12 pages, 8 figures, accepted by Astronomy & Astrophysics; v2 includes 3D calculation and result; v3 includes analysis of numerical simulation, matches accepted versio