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Non-linear CFL Conditions Issued from the von Neumann Stability Analysis for the Transport Equation

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Abstract

This paper presents a theory of the possible non-linear stability conditions encountered in the simulation of convection dominated problems. Its main objective is to study and justify original CFL-like stability conditions thanks to the von Neumann stability analysis. In particular, we exhibit a wide variety of stability conditions of the type \(\Delta t\le C \Delta x^\alpha \) with \(\Delta t\) the time step, \(\Delta x\) the space step, and \(\alpha \) a rational number within the interval [1, 2]. Numerical experiments corroborate these theoretical results.

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Authors and Affiliations

  1. Institut Jean Lamour, Campus Artem, 2 allée André Guinier, BP 50840, 54011, Nancy Cedex, France

    Erwan Deriaz

  2. Laboratoire de Mécanique, Modélisation et Procédés Propres, 38 rue Frédéric Joliot-Curie, 13451, Marseille Cedex 20, France

    Pierre Haldenwang

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  1. Erwan Deriaz
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  2. Pierre Haldenwang
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Correspondence to Erwan Deriaz.

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Deriaz, E., Haldenwang, P. Non-linear CFL Conditions Issued from the von Neumann Stability Analysis for the Transport Equation. J Sci Comput 85, 5 (2020). https://doi.org/10.1007/s10915-020-01302-0

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