A velocity field, even one that represents a steady state flow, implies a dynamical system. Animated velocity fields is an important tool in understanding such complex phenomena. This paper looks at a number of techniques that animate velocity fields and propose two new alternatives. These are texture advection and streamline cycling. The common theme among these techniques is the use of advect...

The Lie derivative, and Exterior Calculus in general, is ubiquitous in the elegant geometric interpretation of many dynamical systems. We extend recent trends towards a Discrete Exterior Calculus by introducing a discrete framework for the Lie derivative defined on differential forms, including a WENO based numerical scheme for its implementation. The usefulness of this operator is demonstrated...

We present a novel method for hardwareaccelerated texture advection of 3D velocity fields defined on curvilinear grids. For uniform rectilinear grids, texture advection can be efficiently performed within the rasterization unit by existing approaches. In a pre-processing step, the vector field is transformed from the curvilinear grid (P-Space) to a uniform rectilinear grid (C-Space). Hardware a...

where a(x, t) is some scalar quantity and u is the velocity at which it is advected (u > 0 advects to the right). The solution to Eq. 1 is to simply take the initial data, a(x, t = 0), and displace it to the right at a speed u. The shape of the initial data is preserved in the advection. Many hyperbolic systems of PDEs, e.g. the equations of hydrodynamics, can be written in a form that looks li...

It is known that the standard Galerkin finite element method (SGFEM) based on low order piecewise polynomials is unsuitable for the solution of steady and unsteady advection diffusion problems. In case the advection term dominates the diffusion one or small time steps are employed, numerical solutions obtained by SGFEM suffer from nonphysical oscillations, unless appropriately designed meshes a...

The interannual variability of the decay of lower stratospheric Arctic vortices is examined using NCEP/NCAR re-analyses between 1958 and 2000. There is large interannual variability in the characteristics of the decay of the vortex air, with very different characteristics for early and late vortex breakups. In early breakup years (when the vortex breaks up in February and early March) the remna...

An oceanic general circulation model is used to investigate the annual cycle of the near-surface currents in the eastern equatorial Pacific Ocean; in particular, the causes of the springtime increase of eastward momentum that reverses the westward surface flow and intensifies the Equatorial Undercurrent are examined. A set of process experiments are carried out that isolates effects due to thre...

Advection-dispersion equation is solved in numerically by using combinations of differential quadrature method (DQM) and various time integration techniques covering some explicit or implicit single and multi step methods. Two different initial boundary value problems modeling conservative and nonconservative transports of some substance represented by initial data are chosen as test problems. ...

Much is known about diffusion-limited growth from a dilute suspension. The simplest and most famous model is diffusion-limited aggregation (DLA), in which random walkers are released one-by-one far away and become frozen where they first touch a growing fractal cluster. Real growth phenomena, such as mineral deposition in rocks, however, often involve multiple processes, such as advection-diffu...