Discontinuous approximation of viscous two-phase flow in heterogeneous porous media

JOURNAL OF COMPUTATIONAL PHYSICS

卷:321

Article

Burger, Raimund^1,3  Kumar, Sarvesh²  Kumar Kenettinkara, Sudarshan³  Ruiz-Baier, Ricardo^1,4 

[1] Univ Concepcion, Dept Ingn Matemat, Casilla 160-C, Concepcion, Chile

[2] Indian Inst Space Sci & Technol, Dept Math, Thiruvananthapuram 695547, Kerala, India

[3] Univ Concepcion, CI2MA, Casilla 160-C, Concepcion, Chile

[4] Univ Oxford, Radcliffe Observ Quarter, Math Inst, Andrew Wiles Bldg,Woodstock Rd, Oxford OX2 6GG, England

关键词: Two phase flow;    Brinkman equations;    Runge-Kutta discontinuous Galerkin methods;    Stabilization;    Finite volume element methods;    Discontinuous fluxes;   

DOI  :  10.1016/j.jcp.2016.05.043

来源: Elsevier

【 摘 要 】

Runge-Kutta Discontinuous Galerkin (RKDG) and Discontinuous Finite Volume Element (DFVE) methods are applied to a coupled flow-transport problem describing the immiscible displacement of a viscous incompressible fluid in a non-homogeneous porous medium. The model problem consists of nonlinear pressure-velocity equations (assuming Brinkman flow) coupled to a nonlinear hyperbolic equation governing the mass balance (saturation equation). The mass conservation properties inherent to finite volume-based methods motivate a DFVE scheme for the approximation of the Brinkman flow in combination with a RKDG method for the spatio-temporal discretization of the saturation equation. The stability of the uncoupled schemes for the flow and for the saturation equations is analyzed, and several numerical experiments illustrate the robustness of the numerical method. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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