Multiscale simulations of porous media flows in flow-based coordinate system

Abstract

In this paper, we propose a multiscale technique for the simulation of porous media flows in a flow-based coordinate system. A flow-based coordinate system allows us to simplify the scale interaction and derive the upscaled equations for purely hyperbolic transport equations. We discuss the applications of the method to two-phase flows in heterogeneous porous media. For two-phase flow simulations, the use of a flow-based coordinate system requires limited global information, such as the solution of single-phase flow. Numerical results show that one can achieve accurate upscaling results using a flow-based coordinate system.

Agglomeration and filtration of colloidal suspensions with DVLO interactions in simulation and experiment

“…The SRD method introduced by Malevanets and Kapral [21] is used for simulating the fluid because it intrinsically contains fluctuations, has low demands for computational time and is applicable to colloidal suspensions [22,28,29,31,51]. SRD is based on calculating the continuous positions of virtual fluid particles at the time t + Dt SRD from the previous positions and velocities.…”

“…The SRD method introduced by Malevanets and Kapral 21 is used for simulating the fluid because it intrinsically contains fluctuations, has low demands for computational time and is applicable to colloidal suspensions 22,28,29,31,51…”

“…The method is also known as multi particle collision dynamics. It has been successfully applied to colloidal suspensions [25][26][27] and flow in confined geometries [26,28,29].…”

Algebraic dynamic multilevel method for embedded discrete fracture model (F-ADM)

“…Multiscale Finite-Element (MsFE) [2][3][4] and Finite-Volume (MsFV) [5][6][7][8][9][10] methods along with Dynamic Local Grid Refinement (DLGR) techniques [11][12][13][14][15][16][17][18][19] are two classes of such advanced methods that aim to achieve accurate and efficient simulations by tackling different aspects of the entire complexity map. Multiscale methods have been developed to efficiently solve the elliptic (or parabolic) pressure equation, which highly heterogeneous coefficients, by solving the system on a coarse grid while preserving the fine-scale heterogeneities.…”