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Report 1996-22
Stability analysis for the method of transport
A.-T. Morel and R. Bodenmann
Abstract: In this paper, we provide analytical stability estimates for the method of transport. We first prove stability of the second-order method of transport applied to the linear advection equation with constant coefficient in one dimension by using the von Neumann method and with the positive operator technique. In a second step, we extend the proof to the linear advection equation with variable coefficient. Finally, we investigate and compare the existing multidimensional schemes from van Leer, Colella, and LeVeque for the linear advection equation with constant coefficients.
Keywords: Multidimensional scheme, method of transport, advection equation, stability, von Neumann method
Paper: Available as PDF (261 KB) or as hardcopy to order reports@sam.math.ethz.ch.
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