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

Erwan Deriaz (1) , Pierre Haldenwang (2)

1 IJL - Institut Jean Lamour
2 M2P2 - Laboratoire de Mécanique, Modélisation et Procédés Propres

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.

Mots clés: CFL condition; von Neumann stability; Transport equation; Runge-Kutta schemes; Finite differences; Turbulence

Domaines: Analyse numérique [math.NA]

Erwan Deriaz, Pierre Haldenwang. Non-linear CFL Conditions Issued from the von Neumann Stability Analysis for the Transport Equation. Journal of Scientific Computing, 2020, 85 (1), pp.5. ⟨10.1007/s10915-020-01302-0⟩. ⟨hal-03231866⟩