Layout optimization of pore microstructure in fluid-saturated porous media using Galerkin decoupling technology and independent continuous mapping method (GDT-ICM)

Abstract

A layout optimal design method combining Galerkin decoupling technology and an independent continuous mapping method (GDT-ICM) is proposed to rearrange the layout of pore microstructure. Firstly, the Galerkin decoupling technology (GDT) is employed to solve the Brinkman equation for fluid flow in fluid-saturated porous media, which integrates the Stokes equation and Darcy's law. Within this framework a self-programmable element balance equation is developed. Secondly, a permeability interpolation function is defined for each element, incorporating the permeability of the fluid and pore microstructure. This function distinguishes strictly between the fluid domain and the pore domain. Pore microstructures with arbitrary shape including permeability information are established in an Euler mesh by introducing the Carman-Kozeny equation, shape functions, the Joukowski mapping and filter functions (a modified arctan mapping function and the MATLAB inpolygon function) based on the ICM method. Thirdly, a layout optimization model aiming at minimizing energy dissipation is established to accomplish the optimal distribution of pore microstructures. A sensitivity analysis is performed with respect to design variables and the optimal model is solved by a genetic algorithm. Numerical results demonstrate that the proposed method is effective and feasible in 2D-space. The maximum velocity within the fluid field is reduced by 45 %, and the issue of localized high pressure occurring around the pore is resolved. This paper provides guidance for solving the Brinkman coupled equation and the layout optimization of the microstructure in porous media.