The multigrid method for discontinuous Galerkin discretizations of advection-diffusion problems is presented. It is based on a block Gauss-Seidel smoother with downwind ordering honoring the advection operator. The cell matrices of the DG scheme are inverted in this smoother in order to obtain robustness for higher order elements. Employing a set of experiments, we show that this technique actu...

Grid-free adaptive semi-Lagrangian advection, as recently suggested in [3], relies on two basic ingredients: scattered data approximation and a customized strategy for the adaption (coarsening and refinement) of the scattered nodes. In this paper, effective rules for the node adaption are proposed. The practicability of the grid-free advection method is illustrated in our numerical examples by ...

We define a family of discrete Advection-reaction operators, denoted by Aaλ, which associate to a given scalar sequence s = {sn} the sequence given by Aaλ(s) ≡ {bn}, where bn = an−2sn−1 + λnsn for n = 1, 2, . . .. For Aaλ we explicitly find their iterates and study their convergence properties. Finally, we show the relationship between the family of discrete operators with the continuous one di...

We analyze the convergence behavior of the overlapping Schwarz waveform relaxation algorithm applied to nonlinear advection problems. We show for Burgers’ equation that the algorithm converges super-linearly at a rate which is asymptotically comparable to the rate of the algorithm applied to linear advection problems. The convergence rate depends on the overlap and the length of the time interv...

The advection of passive tracers in an oscillating vortex chain is investigated. It is shown that by adding a suitable perturbation to the ideal flow, the induced chaotic advection exhibits two remarkable properties which do not hold in the case of a generic perturbation: Particles remain trapped within a specific domain bounded by two oscillating barriers (suppression of chaotic transport alon...

We present an exact mathematical transformation which converts a wide class of advection-diffusion equations into a form allowing simple and direct spatial discretization in all dimensions, and thus the construction of accurate and more efficient numerical algorithms. These discretized forms can also be viewed as master equations which provide an alternative mesoscopic interpretation of advecti...

Abstract. Doppler sonar observations of surface velocity are analysed to extract an rms velocity scale related to flow patterns persisting for at least a minute, and having advection velocities within an adjustable "window" of the mean advection rate. The resulting velocity scale is related to the wind and waves over the course of the twenty days available from the SWAPP data set. The correlati...

We report a 3σ upper limit of 220μJy on any 22-GHz continuum emission coincident with the central engine in NGC 4258. If NGC 4258 is powered by an advection-dominated accretion flow, this radio upper limit implies that the inner advection-dominated flow cannot extend significantly beyond ∼ 10 Schwarzschild radii. Subject headings: accretion, accretion disks — galaxies: active — galaxies: nuclei...

A continuous interior penalty hp-finite element method that penalizes the jump of the gradient of the discrete solution across mesh interfaces is introduced. Error estimates are obtained for advection and advection-diffusion equations. The analysis relies on three technical results that are of independent interest: an hp-inverse trace inequality, a local discontinuous to continuous hp-interpola...

The numerical solutions of the advection-diffusion equation are themselves numerous and sometimes very sophisticated, in order to avoid two undesirable features: oscillatory behavior and numerical diffusion. It is known that the common practice of “splitting-up” the solution is not always the best approach to the advection-diffusion problem. By using the ordinary differential equation analogy m...