A Finite Volume Ventcell-Schwarz Algorithm for Advection-Diffusion Equations

Laurence Halpern (1) , Florence Hubert (2)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 I2M - Institut de Mathématiques de Marseille

This paper provides a new fully discrete domain decomposition algorithm for the advection diffusion reaction equation. It relies on the optimized Ventcell--Schwarz algorithm with a finite volume discretization of the subdomain problems. The scheme includes a wide range of advection fluxes with a special treatment on the boundary. A complete analysis of the scheme is presented, and the convergence of the algorithm to a discrete approximation of the equation using a modified convective flux is proved. Numerical illustrations of the efficiency of the discrete Ventcell--Schwarz algorithm are given.

Mots clés: finite volume methods; optimized Schwarz algorithms; Ventcell boundary conditions

Domaines: Analyse numérique [math.NA]

Laurence Halpern, Florence Hubert. A Finite Volume Ventcell-Schwarz Algorithm for Advection-Diffusion Equations . SIAM Journal on Numerical Analysis, 2014, 52 (3), pp.1269-1291. ⟨10.1137/130919799⟩. ⟨hal-01271249⟩