Improved and enhanced oil recovery' methods require sophisticated simulation tools to predict the injected flow pass together with the chemical reactions inside it. One approach is the application of higher order numerical schemes to avoid excessive numerical diffusion that is very' typical for transport processes. In this work we provide a first step towards higher order schemes applicable on general polyhedral and corner-point grids typically used in reservoir simulation. We compare two possible approaches of linear reconstruction and slope limiting techniques on a variety of different meshes in two and three space dimensions and discuss advantages and disadvantages.
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