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A family of advection schemes is presented for application to element-based finite-volume methods. In these schemes, flow skewness is accounted for by means of a mass flux ratio in a way that positivity is guaranteed. These features assure that the discretization of the advection term does not introduce nonphysical spatial oscillations and reduces to some extent the adverse influence of the grid orientation on the numerical solutions. By means of an analysis of the associated truncation error, the directional properties of the advection schemes are investigated. This analysis and some application examples suggest that one particular scheme in the family yields numerical solutions with minimal influence of the grid topology.
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Hurtado et al. (2012) studied this question.
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