TY - JOUR

T1 - First-order system least squares and the energetic variational approach for two-phase flow

AU - Adler, J. H.

AU - Brannick, J.

AU - Liu, C.

AU - Manteuffel, T.

AU - Zikatanov, L.

N1 - Funding Information:
This work was sponsored by the National Science Foundation under grants, NSF DMS-0810982 , NSF OCI-0749202 , NSF DMS-0707594 , EAR-0621199 , OCI-0749317 , DMS-0811275 , and DMS-0509094 , by the Department of Energy under grant numbers DE-FG02-03ER25574 and DE-FC02-06ER25784 , and by Lawrence Livermore National Laboratory under contract numbers B58858.

PY - 2011/7/20

Y1 - 2011/7/20

N2 - This paper develops a first-order system least-squares (FOSLS) formulation for equations of two-phase flow. The main goal is to show that this discretization, along with numerical techniques such as nested iteration, algebraic multigrid, and adaptive local refinement, can be used to solve these types of complex fluid flow problems. In addition, from an energetic variational approach, it can be shown that an important quantity to preserve in a given simulation is the energy law. We discuss the energy law and inherent structure for two-phase flow using the Allen-Cahn interface model and indicate how it is related to other complex fluid models, such as magnetohydrodynamics. Finally, we show that, using the FOSLS framework, one can still satisfy the appropriate energy law globally while using well-known numerical techniques.

AB - This paper develops a first-order system least-squares (FOSLS) formulation for equations of two-phase flow. The main goal is to show that this discretization, along with numerical techniques such as nested iteration, algebraic multigrid, and adaptive local refinement, can be used to solve these types of complex fluid flow problems. In addition, from an energetic variational approach, it can be shown that an important quantity to preserve in a given simulation is the energy law. We discuss the energy law and inherent structure for two-phase flow using the Allen-Cahn interface model and indicate how it is related to other complex fluid models, such as magnetohydrodynamics. Finally, we show that, using the FOSLS framework, one can still satisfy the appropriate energy law globally while using well-known numerical techniques.

UR - http://www.scopus.com/inward/record.url?scp=79959805136&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79959805136&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2011.05.002

DO - 10.1016/j.jcp.2011.05.002

M3 - Article

AN - SCOPUS:79959805136

SN - 0021-9991

VL - 230

SP - 6647

EP - 6663

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 17

ER -