Premium
Partitioned formulation and stability analysis of a fluid interacting with a saturated porous medium by localised Lagrange multipliers
Author(s) -
Zinatbakhsh S.,
Koch D.,
Park K. C.,
Markert B.,
Ehlers W.
Publication year - 2015
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5148
Subject(s) - lagrange multiplier , stability (learning theory) , compressibility , benchmark (surveying) , porous medium , constraint algorithm , mathematics , scheme (mathematics) , lagrangian , mathematical optimization , mathematical analysis , computer science , porosity , mechanics , physics , materials science , geodesy , machine learning , composite material , geography
Summary In this work, a partitioned scheme for the numerical simulation of the surface‐coupled problem of a fluid interacting with a saturated porous medium (fluid‐porous‐media interaction) is proposed by adopting the method of localised Lagrange multipliers, which facilitates an automatic spatial partitioning of the problem and a parallel treatment of the interacting components, and allows for using tailored solvers optimised for each subproblem. Moreover, proceeding from the interaction between an incompressible bulk fluid with a saturated biphasic porous medium with intrinsically incompressible and inert constituents, the characteristics of the governing equations are scrutinised, and the various constraints within the subsystems are identified. Following this, the method of perturbed Lagrange multipliers is used to replace the constrained equation systems within each subdomain by unconstrained ones. Furthermore, considering the one‐dimensional (1D) version of the equations, a stability analysis of the proposed solution method is performed, and the unconditional stability of the partitioned solution scheme is shown. Solving 1D and 2D numerical benchmark examples, the applicability of the proposed scheme is demonstrated. Copyright © 2015 John Wiley & Sons, Ltd.