Advection multidimensional

Yabusaki, S. B., C. I. Steefel and B. D. Wood, 1998, Multidimensional, multicomponent subsurface reactive transport in non-uniform velocity fields code verification using an advective reactive streamtube approach. Journal of Contaminant Hydrology 30,299-331. 

To understand the behavior of the movement of the contaminant in ground-water, people solve Eq. (1) forward in time. In solving this equation forward in time, one assumes that the plume is originated from somewhere and will travel through the porous media due to advection and dispersion. The conventional procedure to solve Eq. (1) is to use finite difference or finite element methods. For simple cases, closed-form solutions exist. Quantitative descriptions of the processes forward in time are well understood. Multidimensional models of these processes have been used successfully in practice [50]. Numerical solute transport models were first developed about 25 years ago. When properly applied, these models can provide useful information about transport processes and can assist in the design of remedial programs. 

A large number of explicit numerical advection algorithms were described and evaluated for the use in atmospheric transport and chemistry models by Rood [162], and Dabdub and Seinfeld [32]. A requirement in air pollution simulations is to calculate the transport of pollutants in a strictly conservative manner. For this purpose, the flux integral method has been a popular procedure for constructing an explicit single step forward in time conservative control volume update of the unsteady multidimensional convection-diffusion equation. The second order moments (SOM) [164, 148], Bott [14, 15], and UTOPIA (Uniformly Third-Order Polynomial Interpolation Algorithm) [112] schemes are all derived based on the flux integral concept. 

Leonard BP, Lock AP, MacVean MK (1996) Conservative Explicit Unrestricted-Time-Step Multidimensional Constancy-Preserving Advection Schemes. Mon Wea Rev 124 2588-2606... 

Thuburn J (1996) Multidimensional Flux-Limited Advection Schemes. Journal of Computational Physics 123 74-83... 

MACHO Multidimensional Advective Conservative Hybrid Operator MC Monotonic Centered MinMod MinMod function MPI Message Passing Interface... 

Free transport can be seen as a special case of multidimensional advection with u(f,x, ) = However, the absence of a -independent velocity component leads us to consider it separately. 

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