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Stability analysis for the method of transport

by A.-T. Morel and R. Bodenmann

(Report number 1996-22)

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

@Techreport{MB96_205,
  author = {A.-T. Morel and R. Bodenmann},
  title = {Stability analysis for the method of transport},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1996-22},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1996/1996-22.pdf },
  year = {1996}
}

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