Author:

Keywords:

algebraic multigrid, pore network model, moisture transfer, multiscale model

Abstract:

A promising approach to model moisture transfer in porous building materials is pore network modelling, wherein pore-scale physics are applied on a network of pores and throats. The pore network represents the material’s void space and is highly irregular and anisotropic, inherited from the actual pore structure extracted from a micro-CT image. Moreover, porous building materials commonly have a wide pore radius range, from nano- to millimeter, which results in large networks with millions of pores and highly varying coefficients. A direct solver rapidly becomes prohibitively expensive for solving the resulting system of linear equations. To speed up the process we therefore applied various algebraic multigrid (AMG) solvers. In this work, we apply various coarsening methods, smoothers, and cycle types to networks of different size and compare the approaches with respect to CPU time, memory and convergence. AMG performs well in water- and air-saturated conditions, where the matrix of the linear system is symmetric and weakly diagonally dominant. In the dry state, the Ruge-Stüben AMG solver performs better than both a smoothed aggregation and a root-node aggregation technique. In the wet state, root-node aggregation slightly outperforms the other approaches. These observations are mainly related to the homogeneous spatial distribution of the moisture conductivities. The AMG solvers do however not converge as stand-alone methods in the dry-wet transition range. This range is indicated by the early construction of a spanning water cluster connecting in- and outlet. The standard homogeneous coarsening methods fail to adequately represent the dominant localised flow through that continuous water cluster. Using AMG as a preconditioner for GMRES does however significantly enhance the convergence speed. To further increase the computation time, the coarsening methods, interpolations, and smoothers will be adjusted. Alternatively, implementing existing parallel AMG codes in super computer will provide more acceleration.