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1、Grid Peclet NumberThe Peclet number is a non-dimensional term which compares characteristic time for diffusion (dispersion) given a length scale with the characteristic time for advection.The wiggles start at mesh Peclet number above 2 (Unger A.J.A, Forsyth ,P.A. 1995) and the problem becomes more s
2、evere when the Peclet number increase.Courant NumberCourant-Friedrichs-Lewy number, this parameter gives the fractional distance relative to the grid spacing traveled due to advection in a single time stepWith Fourier error analysis it can be shown no matter a scheme (except fully implicit methods)
3、is, it cannot advect a wave more than one grid in each stepDiffusion numberA similar expression may be derived for systems characterized by purely diffusion transport, giving rise to diffusion number: ND1 Amplitude and Phase errorHigh resolution spatial schemesBecause of the great interest in numeri
4、cally simulating high Peclet number transport system (Advection dominant) large numbers of methods have been proposed. These include the method of characteristics or modified versions of it (Konikow and Bredehoeft, 1978; Arbogast et al., 1992; Chilakapati, 1993; Zheng and Bennett 1995; Roache ?) and
5、 adjoint Eulerian-Lagrangian methods (Celia et al. 1990). Both of these approaches are based on the treatment of the advection part of the transport equation using a Lagrangian scheme (a reference frame in which one follows the advective displacement of the fluid packet). An Eulerian (fixed) referen
6、ce frame is then used to simulate dispersive/diffusive transport. The approach reduces numerical dispersion by reducing the effective grid Peclet number for the fixed Eulerian grid. Although there are some implementing restrictions the method of characteristics and its related approaches are still w
7、idely used when it is critical that numerical dispersion be avoided.Another class of high resolution Eulerian methods uses higher-order approximations for the first derivatives, but hybridizes these with low order schemes in an attempt to obtain monotone solutions. The solutions have the higher-orde
8、r approximations in smooth regions and the low-order accuracy near discontinuities (e.g. near plume fronts). The price to be payed for these schemes is that they are non-linear, even when applied to initially linear problem such as ADR equation. In this class are the flux corrected transport (FCT) m
9、ethods (Boris and Book, 1973; Oran and Boris 1987; Zalesak 1987; Hills et al., 1994) which usually gives excellent results when applied to non-reactive solute transport (Hills et al., 1994; Yabusaki et al.,) however, as in some of the other methods discussed here, very low level oscillation still co
10、upled into solution. TVD or total variation diminishing scheme, gives more nearly oscillation-free behavior (Bobey 1984; Yee 1987; Gupta et al. 1991). The TVD is one of a class of methods which use limiters to ensure monotonicity of solution (Van Leer 1977a,b; Leonard ,1984). TVD methods with flux l
11、imiter sometimes performs better than same order FCT counterpart on the reactive transport in case of oscillations (Steefel, C.I., MacQuarrie K.T., 1996)Methods for Coupling Reaction and transport In recent decays much of the discussion about numerical approaches to reactive transport has centered o
12、n the question how to couple the reaction and transport terms. The reaction term affected local concentrations which in turn determine the fluxes of aqueous species. In the same way, the magnitude of the fluxes can affect the reaction rates. An accurate solution of the overall problem therefore requ
13、ires that the terms be coupled at some level. Several methods have been proposed to solve the coupled set of equations. The straightest forward way conceptually, but the most demanding form as computational efficiency point of view, is to solve the governing equations, including both reaction and tr
14、ansport terms, simultaneously . This approach is referred to as a one_step or global implicit method( Kee et al., 1987; Oran and Boris 1987; Steefel and Lasaga, 1994; Steefel and Yabusaki 1996). Alternatively, it is possible to use operator splitting techniques to decoupled set of equations (SNIA: s
15、equential non-iterative approach by T.Xu) consist of solving the reaction and transport equations within a single timestep in sequence, with no iteration between the two. A method championed by Yeh and Tripathi (1989; 1991) is the sequential iteration approach or SIA where the reaction and transport
16、 are solved separately but iteration between the two calculations is carried out until a coverage solution is attained. There are variants on these approaches, including a predictor-corrector approach (Raffensperger and Garven, 1995) and Strang splitting approach (Zysset and Stauffer, 1992).One step or Global Method Since the publication of the influential paper by Yeh and Tripathi (1989) which rejected the use of one-step or glob
