FINITE VOLUME SCHEMES AND LAX-WENDROFF CONSISTENCY

R Eymard (1) , T Gallouët (2) , R Herbin (2) , J.-C Latché (3)

1 Université Gustave Eiffel
2 I2M - Institut de Mathématiques de Marseille
3 IRSN/PSN-RES/SA2I - Service des Agressions Internes et des risques Industriels

We present a (partial) historical summary of the mathematical analysis of finite differences and finite volumes methods, paying a special attention to the Lax-Richtmyer and Lax-Wendroff theorems. We then state a Lax-Wendroff consistency result for convection operators on staggered grids (often used in fluid flow simulations), which illustrates a recent generalization of the flux consistency notion designed to cope with general discrete functions.

Domaines: Analyse numérique [math.NA]

R Eymard, T Gallouët, R Herbin, J.-C Latché. FINITE VOLUME SCHEMES AND LAX-WENDROFF CONSISTENCY. CRAS Compte Rendu Académie des Sciences, 2022, More than a half century of Computational Fluid Dynamics, online first, pp.1-13. ⟨10.5802/crmeca.132.⟩. ⟨hal-03257774v2⟩