Experimental and Numerical Study of Evaporation From Wavy Surfaces by Coupling Free Flow and Porous Media Flow

AbstractDomain decomposition methods are widely used as preconditioners for Krylov subspace linear solvers. In the simulation of porous media flow there has recently been a growing interest in nonlinear preconditioning methods for Newton’s method. In this work, we perform a numerical study of a spatial additive Schwarz preconditioned exact Newton (ASPEN) method as a nonlinear preconditioner for Newton’s method applied to both fully implicit or sequential implicit schemes for simulating immiscible and compositional multiphase flow. We first review the ASPEN method and discuss how the resulting linearized global equations can be recast so that one can use standard preconditioners developed for the underlying model equations. We observe that the local fully implicit or sequential implicit updates efficiently handle the local nonlinearities, whereas long-range interactions are resolved by the global ASPEN update. The combination of the two updates leads to a very competitive algorithm. We illustrate the behavior of the algorithm for conceptual one and two-dimensional cases, as well as realistic three dimensional models. A complexity analysis demonstrates that Newton’s method with a fully implicit scheme preconditioned by ASPEN is a very robust and scalable alternative to the well-established Newton’s method for fully implicit schemes.

Download Full-text

Computational Modeling of Coupled Free and Porous Media Flow for Membrane-based Filtration Systems: A Review

Journal of Applied Membrane Science & Technology ◽

10.11113/amst.v23n3.158 ◽

2019 ◽

Vol 23 (3) ◽

Author(s):

Antonios Parasyris ◽

Christopher Brady ◽

Diganta Bhusan Das ◽

Marco Discacciati

Keyword(s):

Porous Media ◽

Mathematical Models ◽

Fluid Dynamic ◽

Free Flow ◽

Water Filtration ◽

Porous Media Flow ◽

Emergency Situations ◽

Mesoscopic Models ◽

Porous Domain ◽

Flow Domain

We review different mathematical models proposed in literature to describe fluid-dynamic aspects in membrane-based water filtration systems. Firstly, we discuss the societal impact of water filtration, especially in the context of developing countries under emergency situations, and then review the basic concepts of membrane science that are necessary for a mathematical description of a filtration system. Secondly, we categorize the mathematical models available in the literature as (a) microscopic, if the pore-scale geometry of the membrane is accounted for; (b) reduced, if the membrane is treated as a geometrically lower-dimensional entity due to its small thickness compared to the free flow domain; (c) mesoscopic, if the characteristic geometrical dimension of the free flow domain and the porous domain is the same, and a multi-physics problem involving both incompressible fluid flow and porous media flow is considered. Implementation aspects of mesoscopic models in CFD software are also discussed with the help of relevant examples.

Download Full-text