The flux-corrected transport algorithm was implemented on an adaptively refined Cartesian mesh. The error at a mesh-refinement boundary, investigated using Fourier analysis, showed low accuracy when a wave moves from a coarse to a fine mesh. This was improved by using a h'near interpolation between neighbor cells for evaluating convective fluxes. For extension to multidimensions, the flux-corrected transport limiter was modified to take into account information from all the cells facing a mesh-refinement boundary. A series of computations show that the present method simulates a shock wave passing through a mesh-refinement boundary without causing any unphysical waves. Methods for estimating the gain of adaptive mesh refinement, based on available computer memory or computational time, are discussed.
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