Transport algorithms

S.T. Zalesak, Fully Multidimensional Flux-Corrected Transport Algorithms for Fluids, J. Comput. Phys. 31 (1979). 

Van den Berg, A. C. 1980. BLAST—a 1-D variable flame speed blast simulation code using a Flux-Corrected Transport algorithm. Prins Maurits Laboratory TNO report no. PML 1980-162. 

Boris, J. P., Book, D. L., Flux-corrected transport - I. SHASTA, a fluid transport algorithm that works, J. Comput. Phys. 

Note that the empirical PDF in (7.2) depends explicitly on the number of notional particles IV/. However, it also depends implicitly on the number of grid cells (M) through the particle transport algorithm described below. The statistical error associated with estimation of the mean composition (< />) using (7.4) will scale as ,2)/N/)1/2. In zones of the flow where the variance (e//2) is small (e.g., in streams with pure fluid (e/> 2) = 0), Ni can be small However, in zones where mixing and reactions are important, Ni = 100-500 is typically required to obtain particle-number-independent estimates. 

The spatial-transport algorithm is relatively easy to implement on orthogonal grids using information provided by the FV code. 

Relative to Eulerian PDF codes, the spatial-transport algorithm has much higher accuracy. The number of grid cells required for equivalent accuracy is thus considerably smaller. 

The total computational cost is proportional to the number of notional particles (A p), and the spatial-transport algorithm is trivial to parallelize. 

Pfilzner, M., A. Mack, N. Brehm, A. Leonard, and I. Romaschov (1999). Implementation and validation of a PDF transport algorithm with adaptive number of particles in industrially relevant flows. In Computational Technologies for Fluid/Thermal/Structural/Chemical Systems with Industrial Applications, vol. 397-1, pp. 93-104. ASME. 

Coffee, T. P., and J. M. Heimerl. 1981. Transport algorithms for premixed, laminar steady-state flames. Combustion Flame 43 273-89. 

T. Coffee and J.M. Heimerl. Transport Algorithms for Premixed Laminar, Steady-State Flames. Comb. Flame, 43 273-289,1981. 

A. Em and V. Giovangigli. Multicomponent Transport Algorithms. Springer-Verlag, Berlin, 1994. 

Kipp, K.L. Jr., Konikow, L.F., and Hornberger, G.Z., An Imphcit Dispersive Transport Algorithm for the U.S. Geological Survey MOC3D Solute-Transport Model, Water Resources Investigations Report 98-4234, U.S. Geological Survey, Reston, VA, 1998. 

Gaskell, P.H. and Lau, A.K.C. (1988), Curvature - compensated convective transport SMART, A new boundedness preserving transport algorithm, Int. J. Numerical Methods Fluids, 8(6), 617-641. 

Coffee TP, Heimerl JM (1981) Transport Algorithms for Premixed, Laminar Steady-State Flames. Combustion and Flame 43 273-289... 

Boris JP, Book DL (1973) Flux-Corrected Transport. I. SHASTA, A Fluid Transport Algorithm That Works. Journal of Computational Physics, 11 38-69 Bott A (1989) A positive definite advection scheme obtained by nonlinear renormalization of the advective fluxes. Mon Wea Rev 117 1006-1015 Bott A (1989) Reply. Mon Wea Rev 117 2633-2636... 

Gaskell PH, Lau AKC (1988) Curvature-compensated Convective Transport SMART, a new boundedness preserving transport algorithm. Int J Numer Meth Fluids 8 617-641... 

For instance, one inbound and outbound optimization planning software package has the ability to manage shipments from multiple origins to multiple destinations and builds and consolidates loads as orders are imported into the system, using a library of transportation algorithms. Combined with a costing module, it rates, ranks, and selects carriers based on customer needs. 

The computations of the method are rooted in dual linear programming formulation and row operations similar to ones used in Simplex algorithm to solve linear programming problems. We can apply transportation algorithm using the initial solution firom Vogel approximation method. As mentioned in Taha s book [3] multipliers , and y, are associated with row i and column j of transportation table. 

The problem can now be solved by the transportation algorithm. In fact. Example 2.14 can be solved by inspection using a greedy algorithm. That will be discussed in Section 2.17.3. 

Ern, A. Giovangigli, V. (1994). Multicomponent Transport Algorithms, Lect. Notes Phys., Series monographs, M24, Springer-Verlag. 

Zalesak ST (1979) Fully multidimensional flux-corrected transport algorithms for fluids. J Comput Phys 31 335-362... 

In this section, we describe and illustrate an approach for constructing soil-transport parameters, algorithms, and MTCs. The resulting MTCs account for diffusion in gas and liquid components advection in gas, liquid, or solid phases and multiple transformation processes. They also provide an explicit quantification of the characteristic soil penetration depth. We apply transport algorithms to and develop MTCs for both a simple one-layer soil model and more detailed and presumably more realistic multilayer models. 

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