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Mixing, Chaotic Advection, and Turbulence: Annual Review of Fluid Mechanics, Vol. 22, No. 1. (1990), pp. 207-254.add_ab stract_manuall yJM Ottino

Source: Annual Review of Fluid Mechanics, Vol. 22, No. 1. (1990), pp. 207-254.
In situ assembly using a continuous chaotic advection blending process of electrically conducting networks in carbon black-thermopl astic extrusions: Chemical Engineering Science, Vol. 60, No. 8-9. ( 2005), pp. 2459-2467.An industrially relevant continuous flow blending process has been developed that controllably forms in the melt various structured distributions of carbon black particles to impart uniform or directional conductivities to extrusions such as film, sheet, or tubing. A range of electrical properties was selectable on line via process parameter specification. Process control also made possible production of extrusions with graduated or periodic properties such that functional materials and devices can be extracted from extrusions. The process was enabled by chaotic advection, a recent sub-field of fluid mechanics, and was previously demonstrated in part for particulate additives with batch devices. Unlike conventional mixing where the focus is on attaining uniform particle dispersions, chaotic advection inherently promoted structure formation in melts at increasingly smaller length scales such that percolation thresholds can be reduced. Because conducting conditions are attained at low solid additive loadings, a reverse percolation effect was also induced via controlled structure breakdown. Progressive structure formation is related to electrical properties and processing conditions. Methods are applicable to other melt-processab le materials and additives.V Chougule, D Zumbrunnen

Source: Chemical Engineering Science, Vol. 60, No. 8-9. ( 2005), pp. 2459-2467.
Analytical Solution to the Advective-Disp ersive Equation with a Decaying Source and Contaminant: Journal of Hydrologic Engineering, Vol. 13, No. 12. (2008), pp. 1193-1196.Gust avious Williams, David Tomasko

Source: Journal of Hydrologic Engineering, Vol. 13, No. 12. (2008), pp. 1193-1196.
Compact high-resolutio n algorithms for time-dependent advection on unstructured grids: International Journal for Numerical Methods in Fluids, Vol. 33, No. 5. (2000), pp. 711-736.A technique for constructing monotone, high resolution, multi-dimensio nal upwind fluctuation distribution schemes for the scalar advection equation is presented. The method combines the second-order Lax-Wendroff scheme with the upwind positive streamwise invariant (PSI) scheme via a fluctuation redistribution step, which ensures monotonicity (and which is a generalization of the flux-corrected transport approach for fluctuation distribution schemes). Furthermore, the concept of a distribution point is introduced, which, when related to the equivalent equation for the scheme, leads to a ?preferred direction? for the limiting procedure, and hence to a new distribution of the fluctuation, which retains second-order accuracy from the Lax-Wendroff scheme, even when the solution contains turning points. Experimental comparisons show that the new method compares favourably in terms of speed, accuracy and robustness with other, similar, techniques. Copyright © 2000 John Wiley & Sons, Ltd.ME Hubbard, PL Roe

Source: International Journal for Numerical Methods in Fluids, Vol. 33, No. 5. (2000), pp. 711-736.
Consistency with continuity in conservative advection schemes for free-surface models: International Journal for Numerical Methods in Fluids, Vol. 38, No. 4. (2002), pp. 307-327.The consistency of the discretization of the scalar advection equation with the discretization of the continuity equation is studied for conservative advection schemes coupled to three-dimensio nal flows with a free-surface. Consistency between the discretized free-surface equation and the discretized scalar transport equation is shown to be necessary for preservation of constants. In addition, this property is shown to hold for a general formulation of conservative schemes. A discrete maximum principle is proven for consistent upwind schemes. Various numerical examples in idealized and realistic test cases demonstrate the practical importance of the consistency with the discretization of the continuity equation. Copyright © 2002 John Wiley & Sons, Ltd.Edward Gross, Luca Bonaventura, Giorgio Rosatti

Source: International Journal for Numerical Methods in Fluids, Vol. 38, No. 4. (2002), pp. 307-327.
Tracking accuracy of a semi-Lagrangia n method for advection-disp ersion modelling in rivers: International Journal for Numerical Methods in Fluids, Vol. 53, No. 1. (2007), pp. 1-21.There is an increasing need to improve the computational efficiency of river water quality models because: (1) Monte-Carlo-ty pe multi-simulati on methods, that return solutions with statistical distributions or confidence intervals, are becoming the norm, and (2) the systems modelled are increasingly large and complex. So far, most models are based on Eulerian numerical schemes for advection, but these do not meet the requirement of efficiency, being restricted to Courant numbers below unity. The alternative of using semi-Lagrangia n methods, consisting of modelling advection by the method of characteristic s, is free from any inherent Courant number restriction. However, it is subject to errors of tracking that result in potential phase errors in the solutions. The aim of this article is primarily to understand and estimate these tracking errors, assuming the use of a cell-based backward method of characteristic s, and considering conditions that would prevail in practical applications in rivers. This is achieved separately for non-uniform flows and unsteady flows, either via theoretical considerations or using numerical experiments. The main conclusion is that, tracking errors are expected to be negligible in practical applications in both unsteady flows and non-uniform flows. Also, a very significant computational time saving compared to Eulerian schemes is achievable. Copyright © 2006 John Wiley & Sons, Ltd.S Néelz, SG Wallis

Source: International Journal for Numerical Methods in Fluids, Vol. 53, No. 1. (2007), pp. 1-21.
A simple high-resolutio n advection scheme: International Journal for Numerical Methods in Fluids, Vol. 56, No. 5. (2008), pp. 469-484.A simple, robust, mass-conservin g numerical scheme for solving the linear advection equation is described. The scheme can estimate peak solution values accurately even in regions where spatial gradients are high. Such situations present a severe challenge to classical numerical algorithms. Attention is restricted to the case of pure advection in one and two dimensions since this is where past numerical problems have arisen. The authors' scheme is of the Godunov type and is second-order in space and time. The required cell interface fluxes are obtained by MUSCL interpolation and the exact solution of a degenerate Riemann problem. Second-order accuracy in time is achieved via a Runge-Kutta predictor-corr ector sequence. The scheme is explicit and expressed in finite volume form for ease of implementation on a boundary-confo rming grid. Benchmark test problems in one and two dimensions are used to illustrate the high-spatial accuracy of the method and its applicability to non-uniform grids. Copyright © 2007 John Wiley & Sons, Ltd.CG Mingham, DM Causon

Source: International Journal for Numerical Methods in Fluids, Vol. 56, No. 5. (2008), pp. 469-484.
A forward-trajec tory global semi-Lagrangia n transport scheme: J. Comput. Phys., Vol. 190, No. 1. (September 2003), pp. 275-294.Ramach andran Nair, Jeffrey Scroggs, Frederick Semazzi

Source: J. Comput. Phys., Vol. 190, No. 1. (September 2003), pp. 275-294.
Monotonic cascade interpolation for semi-Lagrangia n advection: Quarterly Journal of the Royal Meteorological Society, Vol. 125 (January 1999), pp. 197-212.A simple, more efficient, and more robust form of cascade interpolation is proposed. It significantly reduces the considerable overhead required to determine the mesh points of the intermediate mesh, without degrading accuracy. A simple improvement of an existing monotonic filter is also proposed to address a deficiency and enhance robustness. These ideas are demonstrated using two standard test-problems. R Nair, J Cote, A Staniforth

Source: Quarterly Journal of the Royal Meteorological Society, Vol. 125 (January 1999), pp. 197-212.
SLICE: A Semi-Lagrangia n Inherently Conserving and Efficient scheme for transport problems: Quarterly Journal of the Royal Meteorological Society, Vol. 128 (October 2002), pp. 2801-2820.A Semi-Lagrangia n Inherently Conserving and Efficient (SLICE) scheme is described for transport of passive scalars in Cartesian geometry. It is based on a Control-Volume (CV) approach and uses multiple sweeps of a one-dimensiona l O(x4) conservative remapping algorithm along pre-determined cascade directions. The scheme is applied to standard two-dimensiona l tests from the literature. Overall, it is found that in addition to conserving mass exactly, it is also competitive with standard non-conserving semi-Lagrangia n schemes from the viewpoints of both computational efficiency and accuracy.M Zerroukat, N Wood, A Staniforth

Source: Quarterly Journal of the Royal Meteorological Society, Vol. 128 (October 2002), pp. 2801-2820.

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