DARSim I: Multiscale

"DARSim1 (Multiscale) project aims to develop a multiscale library, MS.lib, extending any existing simulator to benefit from multiscale science."

Selective Relevant Publications

  1. N. Castelletto, H. Hajibeygi, H. A. Tchelepi: Multiscale Finite-Element Method for Linear Elastic Geomechanics, Journal of Computational Physics 331 (2017) 337-356.
  2. M. Tene, M. Al-Kobaisi, H. Hajibeygi: Algebraic multiscale method for flow in heterogeneous porous media with embedded discrete fractures (F-AMS), Journal of Computational Physics, 321 (15) 819-845.
  3. S. Shah, O. Moyner, M. Tene, K-A. Lie, H. Hajibeygi, The multiscale restriction smoothed basis method for fractured porous media (F-MsRSB), Journal of Computational Physics, 318 (2016) 36–57.
  4. M. Cusini, A. Lukyanov, J. Natvig, H. Hajibeygi: Constrained pressure residual multiscale (CPR-MS) method for fully implicit simulation of multiphase flow in porous media, Journal of Computational Physics, 2015.
  5. M. Tene, Y. Wang, H. Hajibeygi, Adaptive Algebraic Multiscale Solver for Compressible Flows in Heterogeneous Porous Media, Journal of Computational Physics, 300 (2015) 679-694.
  6. Y. Wang, H. Hajibeygi, H. A. Tchelepi: Monotone Multiscale Finite-Volume Method, Computational Geosciences, Computational Geosciences, 20 (2016), 509-524.
  7. H. Hajibeygi, H. A. Tchelepi: Compositional Multiscale Finite-Volume Formulation, SPE Journal, 19 (2014) 316-326.
  8. Y. Wang, H. Hajibeygi, H. A. Tchelepi, Algebraic multiscale solver for flow in heterogeneous porous media, Journal of Computational Physics, Volume 259, 15 February 2014, Pages 284–303.
  9. H. Hajibeygi, S. H. Lee and I. Lunati: Accurate and Efficient Simulation of Multiphase Flow in a Heterogeneous Reservoir by Using Error Estimate and Control in the Multiscale Finite-Volume Framework, SPE Journal, 17 (2012) 1071-1083.
  10. H. Hajibeygi, D. Karvounis and P. Jenny: A hierarchical fracture model for the iterative multiscale finite volume method, Journal of Computational Physics, 230 (2011) 8729-8743.
  11. H. Hajibeygi and P. Jenny: Adaptive iterative multiscale finite volume method, Journal of Computational Physics, 230 (2011), 628-643.
  12. H. Hajibeygi and P. Jenny: Multiscale finite volume method for parabolic problems arising from compressible multiphase flow in porous media, Journal of Computational Physics, 228 (2009) 5129-5147.
  13. H. Hajibeygi, G. Bonfigli, M.A. Hesse, and P. Jenny: Iterative multiscale finite-volume method, Journal of Computational Physics 227 (2008) 8604-8621.
  14. A. Lukyanov, H. Hajibeygi, J. Natvig, K. Bradtvet: MULTILEVEL MONOTONE CONSTRAINED PRESSURE RESIDUAL MULTISCALE TECHNIQUES, US 2016/0162612, 2016.


Accurate and efficient numerical simulation of multiphase flow in natural formations is highly important for understanding their history and providing reliable predictive engineering strategies for maximizing profit and safety factors. High-resolution data, integrated by geo-scientists, need to be fully taken into account for such numerical simulations. However, due to the large length scales of the formation (km), high-resolution data cannot be incorporated in the state-of-the-art simulators. To avoid using excessively upscaled parameters, which often lead to inaccurate and unreliable management strategies, multiscale modeling and simulation methods have been developed.

One of the main projects of DARSim team is to advance frontiers of multiscale methods and put them in practice of next-generation simulation framework. This project does not only involves method developments, but also a smart algebraic implementation which allows for easy integration of the developments into any existing and next-generation simulators. Our multiscale library (MS.lib) can be released to our scientific partners and sponsors. This library has been developed based on our recent papers, the performance of which has been benchmarked with commercial solvers. Note that MS.lib is a research-based library, aimed to develop for years to come! Below, a brief scientific overview of multiscale methods is provided. A multiscale method allows for accurate and efficient simulation of a heterogeneous problem by using a lot less degrees of freedom (for the below example, 4x4 instead of 44x44):

Algebraic Multiscale Solver (AMS and C-AMS) for multiphase flows with complex physics and geometries

We developed Algebraic Multiscale Solver for Incompressible (AMS) and Compressible (C-AMS) Flows. These papers are the first of their type in the filed, in the sense that they published the CPU time of AMS and C-AMS compared with those of an industrial-grade AMG Solver for prblem sizes up to 20 Million Cells (shown below).

Monotone Multiscale Finite Volume Method (m-MSFV) for multiphase flows in highly heterogeneous media

In addition to the AMS and C-AMS, it has been known that the MSFV results in non-monotone solutions in presence of highly heterogeneous permeability fields. Though one can reduce the non-physical peaks by iterations of i-MSFV or C-AMS; it is crucial to avoid these nonphysical peaks from happening than to resolve them by the cost of iterations. Therefore, recently we developed a monotone MSFV (m-MSFV) method which guarantees the monotonicity of the MSFV solutions for highly heterogeneous fields.

Multiscale Simulation of Compositional Displacements

We recently developed the first multiscale formulation for compositional flows. Results of this work is published in the relevant reference given above.

Fully Implicit Multiscale Simulation

Recently we developed the first multiscale method for fully implicit simulation of multiphase flows in heterogeneous media. The work shed new light in the application of multiscale methods, which was done together with Matteo Cusini and our collaborators at Schlumberger Company, INTERSECT team, Alex and Jostein.

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