Finite volume method for coupled subsurface flow problems, I: Darcy problem
Terekhov K. M., Vasilevskij Yu. V.
Journal of Computational Physics
Vol.395, P. 298-306
Опубликовано: 2019
Тип ресурса: Статья
DOI:10.1016/j.jcp.2019.06.009
Аннотация:
The article introduces a finite-volume method for the Darcy problem in heterogeneous anisotropic media. The method is based on the mixed formulation for the pressure and its gradient. The method is stable despite collocation of both pressure and its gradient at cell centers and demonstrates the first order convergence on numerous benchmarks as well as good monotonicity property. The method produces quasi-definite matrix, which is numerically shown to have good asymptotics of the condition number. Our flux discretization method is a realization of our more general concept of stable flux discretization for saddle-point systems with vector of several unknowns. In this paper this vector is composed of pressure and its gradient and the saddle-point system is the mixed formulation of the Darcy problem. © 2019 Elsevier Inc.
Ключевые слова:
Anisotropic diffusion; Darcy problem; Finite-volume; Saddle-point
Anisotropic media; Anisotropy; Discrete event simulation; Finite volume method; Number theory; Anisotropic Diffusion; Condition numbers; Darcy problem; Discretization method; Mixed formulations; Monotonicity property; Saddle point; Saddle point system; Flow of fluids
Язык текста: Английский
ISSN: 1090-2716
Terekhov K. M.
Vasilevskij Yu. V. Yurij Viktorovich 1967-
Терехов К. М.
Василевский Ю. В. Юрий Викторович 1967-
Finite volume method for coupled subsurface flow problems, I: Darcy problem
Текст визуальный непосредственный
Journal of Computational Physics
Academic Press
Vol.395 P. 298-306
2019
Статья
Anisotropic diffusion Darcy problem Finite-volume Saddle-point
Anisotropic media Anisotropy Discrete event simulation Finite volume method Number theory Anisotropic Diffusion Condition numbers Darcy problem Discretization method Mixed formulations Monotonicity property Saddle point Saddle point system Flow of fluids
The article introduces a finite-volume method for the Darcy problem in heterogeneous anisotropic media. The method is based on the mixed formulation for the pressure and its gradient. The method is stable despite collocation of both pressure and its gradient at cell centers and demonstrates the first order convergence on numerous benchmarks as well as good monotonicity property. The method produces quasi-definite matrix, which is numerically shown to have good asymptotics of the condition number. Our flux discretization method is a realization of our more general concept of stable flux discretization for saddle-point systems with vector of several unknowns. In this paper this vector is composed of pressure and its gradient and the saddle-point system is the mixed formulation of the Darcy problem. © 2019 Elsevier Inc.