Numerical Multilevel Upscaling for Incompressible Flow in Reservoir Simulation: An Element-Based Algebraic Multigrid (AMGe) Approach
- Technical Univ. of Denmark, Lyngby (Denmark); Technical Univ. of Denmark, Lloyd's Register Consulting, Hellerup (Denmark)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); The Univ. of Texas at Austin, Austin, TX (United States)
- Technical Univ. of Denmark, Lyngby (Denmark)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Here, we study the application of a finite element numerical upscaling technique to the incompressible two-phase porous media total velocity formulation. Specifically, an element-agglomeration-based algebraic multigrid (AMGe) technique with improved approximation properties is used, for the first time, to generate upscaled and accurate coarse systems for the reservoir simulation equations. The upscaling technique is applied to both the mixed system for velocity and pressure and to the hyperbolic transport equations, providing fully upscaled systems. By introducing additional degrees of freedom associated with nonplanar interfaces between agglomerates, the coarse velocity space has guaranteed approximation properties. The employed AMGe technique provides coarse spaces with desirable local mass conservation and stability properties analogous to the original pair of Raviart--Thomas and piecewise discontinuous polynomial spaces, resulting in strong mass conservation for the upscaled systems. Due to the guaranteed approximation properties and the generic nature of the AMGe method, recursive multilevel upscaling is automatically obtained. Furthermore, this technique works for both structured and unstructured meshes. Multiscale mixed finite elements exhibit accuracy for general unstructured meshes but do not in general lead to nested hierarchy of spaces. Multiscale multilevel mimetic finite differences generate nested spaces but lack the adaptivity of the flux representation on coarser levels that the proposed AMGe approach offers. Thus, the proposed approach can be seen as a rigorous bridge that merges the best properties of these two existing methods. The accuracy and stability of the studied multilevel AMGe upscaling technique is demonstrated on two challenging test cases.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- Grant/Contract Number:
- AC52-07NA27344
- OSTI ID:
- 1461736
- Report Number(s):
- LLNL-JRNL-661295; 782221
- Journal Information:
- SIAM Journal on Scientific Computing, Vol. 39, Issue 1; ISSN 1064-8275
- Publisher:
- SIAMCopyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
Scalable hierarchical PDE sampler for generating spatially correlated random fields using nonmatching meshes: Scalable hierarchical PDE sampler using nonmatching meshes
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journal | January 2018 |
| Scalable hierarchical PDE sampler for generating spatially correlated random fields using non-matching meshes | preprint | January 2017 |
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