Non-linear CFL Conditions Issued from the von Neumann Stability Analysis for the Transport Equation
Résumé
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 t ≤ C x α with t the time step, x the space step, and α a rational number within the interval [1, 2]. Numerical experiments corroborate these theoretical results.
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