Abstract: Fey's Method of Transport (MoT) is a multi-dimensional flux-vector-splitting scheme for systems of conservation laws. Similarly to its one-dimensional fore-runner, the Steger-Warming scheme, and several other upwind finite difference schemes, the MoT suffers from an inconsistency at sonic points when used with piecewise-constant reconstructions. This inconsistency is due to a Cell-Centered-Evolution-Scheme, which we call MoT-CCE, that is used to propagate the waves resulting from the flux-vector-splitting step. Here we derive new first-order- and second-order-consistent characteristic schemes based on Interface-Centered-Evolution, which we call MoT-ICE. We prove consistency at all points, including the sonic points. Moreover, we simplify Fey's wave-decomposition by distinguishing clearly between a linearisation and a decomposition step. Numerical experiments confirm the stability and accuracy of the new schemes. Due to the simplicity of the two new ingredients of the MoT-ICE, its second-order version is several times faster than that of the MoT-CCE.
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