Accurate multi-level schemes for advection

The upwind leapfrog method for the advection equation, which is non-dissipative and very accurate, is extended to higher-order and multiple dimensions. The higher-order version is developed by extending the stencil into space and time, and an analysis of the phase error is given. The schemes are then successfully applied to the classical test cases of rotating flow, and to a more realistic problem of non-uniform advection.