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In order to investigate effects of the dynamic capillary pressure-saturation relationship used in the modelling of a flow in porous media, a one-dimensional fully implicit numerical scheme is proposed. The numerical scheme is used to simulate an experimental procedure using a measured dataset for the sand and fluid properties. Results of simulations using different models for the dynamic effect term in capillary pressure-saturation relationship are presented and discussed.
We derive error estimates for singularly
perturbed reaction–diffusion problems which yield a guaranteed
upper bound on the discretization error and are fully and easily
computable. Moreover, they are also locally efficient and robust in
the sense that they represent local lower bounds for the actual
error, up to a generic constant independent in particular of the
reaction coefficient. We present our results in the framework of
the vertex-centered finite volume method but their nature is
general...
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