A finite element formulation of the outlet gradient boundary condition for convective-diffusive transport problems

Details A finite element formulation of the outlet gradient boundary condition for convective-diffusive transport problems A finite element formulation of the outlet gradient boundary condition for convective-diffusive transport problems

2011-08-28

arxiv.org/abs/1108.5482v1

Int. J. Numer. Meth. Engng 2004; 61:2716-2732

Physics

Fluid Dynamics

17 pages, 8 figures

Scientific paper

10.1002/nme.1188

A simple finite element formulation of the outlet gradient boundary condition is presented in the general context of convective-diffusive transport processes. Basically, the method is based on an upstream evaluation of the dependent variable gradient along open boundaries. Boundary normal unit vectors and gradient operators are evaluated using covariant bases and metric tensors, which allow handling finite elements of mixed dimensions. Even though the presented method has implications for many fields where diffusion processes are involved, discussion and illustrative examples address more particularly the framework of contaminant transport in porous media, in which the outlet gradient concentration is classically, but wrongly assumed to be zero.

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