A finite volume preserving scheme on nonuniform meshes and for multidimensional coalescence

Louis Forestier-Coste (1) , Simona Mancini (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

In this paper we present a deterministic numerical approximation of the coalescence or Smoluchowski equation. Our numerical scheme conserves the first order momentum and deals with nonuniform grids. The generalization to a multidimensional framework is also described. We validate the scheme considering some classical tests both in one and two dimensions and discuss its behavior when gelation occurs. Our numerical results and code are compared with those already existent in the literature.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Louis Forestier-Coste, Simona Mancini. A finite volume preserving scheme on nonuniform meshes and for multidimensional coalescence. SIAM Journal on Scientific Computing, 2012, pp.B840-B860. ⟨10.1137/110847998⟩. ⟨hal-00621069v2⟩