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The relationship between two approaches towards construction of genuinely two-dimensional upwind advection schemes is established. One of these approaches is of the control volume type applicable on structured cartesian meshes. It resulted in the compact high resolution schemes capable of maintaining second order accuracy in both homogeneous and inhomogeneous cases. Another one is the fluctuation splitting approach, which is well suited for triangular (and possibly) unstructured meshes. Understanding the relationship between these two approaches allows us to formulate here a new fluctuation splitting high resolution (i.e. possible use of artificial compression, while maintaining positivity property) scheme. This scheme is shown to be linearity preserving in inhomogeneous as well as homogeneous cases.

In this paper a relationship between two approaches towards construction of genuinely two-dimensional upwind advection schemes is established. One of these approaches is of the control volume type applicable on structured cartesian meshes. It resulted (see 14. 15) in the compact high resolution schemes capable of maintaining second order accuracy in both homogeneous and inhomogeneous cases. Another one is the fluctuation splitting approach (see 11 3 12 17). which is well suited for triangular (and possibly) unstructured meshes. Understanding the relationship between these two approaches allows us to formulate here a new fluctuation splitting high resolution (i.e. possible use of artificial compression while maintaining positivity property) scheme. This scheme is shown to be linearity preserving in inhomogeneous as well as homogeneous cases.