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

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.

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⟩

Journal: Journal of Scientific Computing

Date de publication: 01-01-2020

Auteurs:
  • Erwan Deriaz
  • Pierre Haldenwang

Digital object identifier (doi): http://dx.doi.org/10.1007/s10915-020-01302-0


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