Event
01_1
| 제출번호(No.) | 0117 |
|---|---|
| 분류(Section) | Poster Session |
| 분과(Session) | Applied Mathematics (AM) |
| 영문제목 (Title(Eng.)) |
Efficient uniform grids based numerical methods for two-phase flows in heterogeneous porous media using multigrid solver |
| 저자(Author(s)) |
Gwanghyun Jo1, Do Young Kwak1 KAIST1 |
| 초록본문(Abstract) | Multiphase flows in porous media is of importance in various disciplines especially in petroleum engineering. However, in subsurface porous media, the material properties vary abruptly along the interface. These makes the governing equations difficult to solve numerically since they contain discontinuous coefficients. For example, permeability, porosity, capillary pressure may be discontinuous. Conventional numerical methods (control volume, finite element/volume methods, discontinuous Galerkin methods) to solve problems with interface are based on fitted grids. However, fitted grids based methods yields complex data structure. This makes the multigrid algorithms not available. However, there exists some new developments in finite element methods (FEM) community. The so called immersed FEM (IFEM) which use uniform grids for interface problems are developed. One of the big advantage of the IFEM is that multigrids algorithms are available, since IFEM use uniform grids. In this presentation, we show the numerical methods for porous media using IFEM [1]. The pressure equations are solved effectively by using IFEM and velocity are solved in mixed finite volume frameworks. The saturation variables are solved in Euler forward methods. To enhance the efficiency, saturations are solved by control volume with upwinding schemes. Also, we show how we apply multigrid solvers. The numerical results show that our methods are of optimal for pressure and velocity and suboptimal for saturation variable. The time cost for the methods are O(N) where N is number of pressure variables since we apply multigrid solvers. [1] Jo, Gwanghyun, and Do Y. Kwak. "An IMPES scheme for a two-phase flow in heterogeneous porous media using a structured grid." Computer Methods in Applied Mechanics and Engineering 317 (2017): 684-701. |
| 분류기호 (MSC number(s)) |
37N10, 65M55 |
| 키워드(Keyword(s)) | porous media, multiphase flows, immersed FEM, multigrid solver |
| 강연 형태 (Language of Session (Talk)) |
Korean |