Efficient Implementation of High Order Reconstruction in Finite Volume Methods

Florian Haider (1) , Jean-Pierre Croisille (2) , Bernard Courbet (1)

1 ONERA - The French Aerospace Lab [Châtillon]
2 LMAM - Laboratoire de Mathématiques et Applications de Metz

This paper shows how to compute a high order approximant in a given cell using only data from adjacent cells at a time, eliminating the need to handle directly large reconstruction stencils. No additional degrees of freedom are added: the independent variables are the cell averages of the conserved quantity. The resulting high order finite volume method is well suited for modern parallel and vector (array) computers. This aspect is of primary importance for large scale industrial software.

Domaines: Milieux fluides et réactifs; Calcul parallèle, distribué et partagé [cs.DC]; Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Florian Haider, Jean-Pierre Croisille, Bernard Courbet. Efficient Implementation of High Order Reconstruction in Finite Volume Methods. Finite Volumes for Complex Applications : problems and perspectives, Jun 2011, Prague, Czech Republic. pp.553-562, ⟨10.1007/978-3-642-20671-9_58⟩. ⟨hal-01283666⟩