L'IMplicit Pressure Explicit Saturation method (IMPES) est l'une des principales méthodes pour traiter les cas d'écoulements multiphasiques en milieu poreux. La stabilité numérique de cette méthode séquentielle implique des contraintes différentes sur le pas de temps selon le régime d'écoulement étudié. Dans cette note, les trois principaux critères de stabilité liés à l'IMPES sont testés sur des milieux homogènes et hétérogènes pour différents régimes (visqueux/capillaire/gravitaire). Cette étude montre qu'aucun critère optimal, réunissant stabilité et efficacité, ne se dégage. Pour les écoulements capillaires, la condition de Todd est la plus efficace, tandis que la condition standard de Coats est préférable pour les écoulements visqueux. Quand les effets gravitaires sont pris en compte, la condition de Coats doit être restreinte, mais demeure plus efficace que celle de Todd.
The IMplicit Pressure Explicit Saturation (IMPES) method is a prevalent way to simulate multiphase flows in porous media. The numerical stability of this sequential method implies limitations on the time step, which may depend on the flow regime studied. In this note, three stability criteria related to the IMPES method, that differ in their construction on the observed variables, are compared on homogeneous and heterogeneous configurations for different two-phase flow regimes (viscous/capillary/gravitational). This highlights that there is no single optimal criterion always ensuring stability and efficiency. For capillary dominated flows, the Todd's condition is the most efficient one, while the standard Coat condition should be preferred for viscous flows. When gravity effects are present, Coat's condition must be restricted, but remains more efficient than the Todd's condition.
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Mot clés : IMPES, Critère de stabilité, CFL, Écoulements multiphasiques, Milieux Poreux, Efficacité numérique
Jacques Franc 1, 2 ; Pierre Horgue 1, 2 ; Romain Guibert 1, 2 ; Gerald Debenest 1, 2
@article{CRMECA_2016__344_10_715_0, author = {Jacques Franc and Pierre Horgue and Romain Guibert and Gerald Debenest}, title = {Benchmark of different {CFL} conditions for {IMPES}}, journal = {Comptes Rendus. M\'ecanique}, pages = {715--724}, publisher = {Elsevier}, volume = {344}, number = {10}, year = {2016}, doi = {10.1016/j.crme.2016.08.003}, language = {en}, }
TY - JOUR AU - Jacques Franc AU - Pierre Horgue AU - Romain Guibert AU - Gerald Debenest TI - Benchmark of different CFL conditions for IMPES JO - Comptes Rendus. Mécanique PY - 2016 SP - 715 EP - 724 VL - 344 IS - 10 PB - Elsevier DO - 10.1016/j.crme.2016.08.003 LA - en ID - CRMECA_2016__344_10_715_0 ER -
Jacques Franc; Pierre Horgue; Romain Guibert; Gerald Debenest. Benchmark of different CFL conditions for IMPES. Comptes Rendus. Mécanique, Volume 344 (2016) no. 10, pp. 715-724. doi : 10.1016/j.crme.2016.08.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.08.003/
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