{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:36:53Z","timestamp":1760060213990,"version":"build-2065373602"},"reference-count":87,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,8]],"date-time":"2025-08-08T00:00:00Z","timestamp":1754611200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100008982","name":"Qatar National Research Fund","doi-asserted-by":"publisher","award":["ARG 01-0502-230056"],"award-info":[{"award-number":["ARG 01-0502-230056"]}],"id":[{"id":"10.13039\/100008982","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Efficient simulation of multiphase, multicomponent fluid flow in heterogeneous reservoirs is critical for optimizing hydrocarbon recovery. In this study, we investigate advanced linearization techniques for fully implicit compositional reservoir simulations, a problem characterized by highly nonlinear governing equations that challenge both accuracy and computational efficiency. We implement four methods\u2014finite backward difference (FDB), finite central difference (FDC), operator-based linearization (OBL), and residual accelerated Jacobian (RAJ)\u2014within an MPI-based parallel framework and benchmark their performance against a legacy simulator across three test cases: (i) a five-component hydrocarbon gas field with CO2 injection, (ii) a ten-component gas field with CO2 injection, and (iii) a ten-component gas field case without injection. Key quantitative findings include: in the five-component case, OBL achieved convergence with only 770 nonlinear iterations (compared to 841\u2013843 for other methods) and reduced operator computation time to 9.6 of total simulation time, highlighting its speed for simpler systems; in contrast, for the more complex ten-component injection, FDB proved most robust with 706 nonlinear iterations versus 723 for RAJ, while OBL failed to converge; in noninjection scenarios, RAJ effectively captured nonlinear dynamics with comparable iteration counts but lower overall computational expense. These results demonstrate that the optimal linearization strategy is context-dependent\u2014OBL is advantageous for simpler problems requiring rapid solutions, whereas FDB and RAJ are preferable for complex systems demanding higher accuracy. The novelty of this work lies in integrating these advanced linearization schemes into a scalable, parallel simulation framework and providing a comprehensive, quantitative comparison that extends beyond previous efforts in reservoir simulation literature.<\/jats:p>","DOI":"10.3390\/computation13080191","type":"journal-article","created":{"date-parts":[[2025,8,8]],"date-time":"2025-08-08T08:09:35Z","timestamp":1754640575000},"page":"191","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Advanced Linearization Methods for Efficient and Accurate Compositional Reservoir Simulations"],"prefix":"10.3390","volume":"13","author":[{"given":"Ali","family":"Asif","sequence":"first","affiliation":[{"name":"Division of Sustainable Development, College of Science and Engineering, Hamad Bin Khalifa University, Education City, Qatar Foundation, Doha P.O. Box 5825, Qatar"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abdul Salam","family":"Abd","sequence":"additional","affiliation":[{"name":"Division of Sustainable Development, College of Science and Engineering, Hamad Bin Khalifa University, Education City, Qatar Foundation, Doha P.O. Box 5825, Qatar"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ahmad","family":"Abushaikha","sequence":"additional","affiliation":[{"name":"Division of Sustainable Development, College of Science and Engineering, Hamad Bin Khalifa University, Education City, Qatar Foundation, Doha P.O. Box 5825, Qatar"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3303","DOI":"10.1016\/j.camwa.2019.05.002","article-title":"Simulation of multi-component multi-phase fluid flow in two-dimensional anisotropic heterogeneous porous media using high-order control volume distributed methods","volume":"78","author":"Moshiri","year":"2019","journal-title":"Comput. Math. Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1797","DOI":"10.1002\/fld.2665","article-title":"A family of multi-point flux approximation schemes for general element types in two and three dimensions with convergence performance","volume":"69","author":"Pal","year":"2012","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Zhou, Y., Tchelepi, H.A., and Mallison, B.T. (2011, January 21\u201323). Automatic differentiation framework for compositional simulation on unstructured grids with multi-point discretization schemes. Proceedings of the SPE Reservoir Simulation Conference, The Woodlands, TX, USA.","DOI":"10.2118\/141592-MS"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"436","DOI":"10.2118\/106445-PA","article-title":"A mimetic finite volume discretization method for reservoir simulation","volume":"15","author":"Alpak","year":"2010","journal-title":"SPE J."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"131675","DOI":"10.1016\/j.jhydrol.2024.131675","article-title":"Diffusion hysteresis in unsaturated porous media: A microfluidic study","volume":"640","author":"Zhuang","year":"2024","journal-title":"J. Hydrol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.geothermics.2018.01.012","article-title":"Operator-based linearization for efficient modeling of geothermal processes","volume":"74","author":"Khait","year":"2018","journal-title":"Geothermics"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1016\/j.jngse.2017.07.031","article-title":"Nonlinearity and solution techniques in reservoir simulation: A review","volume":"46","author":"Deb","year":"2017","journal-title":"J. Nat. Gas Sci. Eng."},{"key":"ref_8","unstructured":"Cao, H. (2002). Development of Techniques for General Purpose Simulators, Stanford University."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Wang, Y., Luther, J., Jenny, D., Immer, M., and Jenny, P. (2025, March 05). Space-Time Adaptive Conservative Finite Volume Scheme for Unsteady Compressible Flow. Available online: https:\/\/papers.ssrn.com\/sol3\/papers.cfm?abstract_id=5119570.","DOI":"10.2139\/ssrn.5119570"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"316","DOI":"10.2118\/52051-PA","article-title":"Linearization techniques of reservoir-simulation equations: Fully implicit cases","volume":"3","author":"Farkas","year":"1998","journal-title":"SPE J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"113558","DOI":"10.1016\/j.jcp.2024.113558","article-title":"Compositional reservoir simulation with a high-resolution compact stencil adaptive implicit method","volume":"521","author":"Deucher","year":"2025","journal-title":"J. Comput. Phys."},{"key":"ref_12","unstructured":"Mohebbinia, S. (2013, January 18\u201320). Advanced equation of state modeling for compositional simulation of gas floods. Proceedings of the SPE Reservoir Simulation Conference, The Woodlands, TX, USA."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Rin, R. (2017). Implicit Coupling Framework for Multi-Physics Reservoir Simulation. [Ph.D. Thesis, Stanford University].","DOI":"10.2118\/182714-MS"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/0167-8191(90)90069-L","article-title":"MIMD implementations of linear solvers for oil reservoir simulation","volume":"16","author":"Baker","year":"1990","journal-title":"Parallel Comput."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"417","DOI":"10.2118\/2185-PA","article-title":"Solution of two-phase flow problems using implicit difference equations","volume":"9","author":"Blair","year":"1969","journal-title":"Soc. Pet. Eng. J."},{"key":"ref_16","unstructured":"Aziz, K., and Wong, T. (1989, January 4\u20138). Considerations in the development of multipurpose reservoir simulation models. Proceedings of the First and Second Forum on Reservoir Simulation, Alpbach, Austria."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1016\/j.jcp.2017.06.034","article-title":"Fully implicit mixed-hybrid finite-element discretization for general purpose subsurface reservoir simulation","volume":"346","author":"Abushaikha","year":"2017","journal-title":"J. Comput. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"109004","DOI":"10.1016\/j.icheatmasstransfer.2025.109004","article-title":"Insight into the permeability effect on forced convective heat transfer characteristics in porous media based on the pore-scale numerical study","volume":"165","author":"Yang","year":"2025","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_19","unstructured":"Bosma, S.B.M. (2021). Algorithms and Discretization Schemes for Efficient Simulation of Multiphase Flow and Transport in Porous Media, Stanford University."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"103","DOI":"10.2118\/3174-PA","article-title":"Use of irregular grid in reservoir simulation","volume":"12","author":"Settari","year":"1972","journal-title":"Soc. Pet. Eng. J."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Sun, J., Sun, R., Qiao, P., Tan, S., and Tian, R. (2025, May 25). Numerical Study of Bi-Stable Flow Phenomena in Square Tube Bundles Based on Refined Modelling Method. Available online: https:\/\/papers.ssrn.com\/sol3\/papers.cfm?abstract_id=5264819.","DOI":"10.2139\/ssrn.5264819"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"819","DOI":"10.1007\/s10596-019-09841-8","article-title":"Optimization of CO2 injection using multi-scale reconstruction of composition transport","volume":"24","author":"Chen","year":"2020","journal-title":"Comput. Geosci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1029\/94WR00061","article-title":"Accuracy of mixed and control volume finite element approximations to Darcy velocity and related quantities","volume":"30","author":"Durlofsky","year":"1994","journal-title":"Water Resour. Res."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/0045-7825(92)90186-N","article-title":"A control volume method to solve an elliptic equation on a two-dimensional irregular mesh","volume":"100","author":"Faille","year":"1992","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"744","DOI":"10.1016\/j.jcp.2004.10.002","article-title":"Discretization on quadrilateral grids with improved monotonicity properties","volume":"203","author":"Nordbotten","year":"2005","journal-title":"J. Comput. Phys."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2082","DOI":"10.1137\/050638473","article-title":"A multipoint flux mixed finite element method","volume":"44","author":"Wheeler","year":"2006","journal-title":"SIAM J. Numer. Anal."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1016\/j.apm.2019.01.033","article-title":"A new multipoint flux approximation method with a quasi-local stencil (MPFA-QL) for the simulation of diffusion problems in anisotropic and heterogeneous media","volume":"70","author":"Contreras","year":"2019","journal-title":"Appl. Math. Model."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1438","DOI":"10.1002\/num.20158","article-title":"Convergence of multipoint flux approximations on quadrilateral grids","volume":"22","author":"Klausen","year":"2006","journal-title":"Numer. Methods Partial. Differ. Equ. Int. J."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Aavatsmark, I., Eigestad, G.T., and Klausen, R.A. (2006). Numerical convergence of the MPFA O-method for general quadrilateral grids in two and three dimensions. Compatible Spatial Discretizations, Springer.","DOI":"10.1007\/s10596-007-9056-8"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"658","DOI":"10.2118\/106435-PA","article-title":"A new finite-volume approach to efficient discretization on challenging grids","volume":"15","author":"Aavatsmark","year":"2010","journal-title":"SPE J."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.cam.2015.02.051","article-title":"A robust linearization scheme for finite volume based discretizations for simulation of two-phase flow in porous media","volume":"289","author":"Radu","year":"2015","journal-title":"J. Comput. Appl. Math."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1858","DOI":"10.2118\/205378-PA","article-title":"Operator-based linearization approach for modeling of multiphase flow with buoyancy and capillarity","volume":"26","author":"Lyu","year":"2021","journal-title":"SPE J."},{"key":"ref_33","first-page":"28","article-title":"Reservoir simulation","volume":"213","author":"Batycky","year":"1958","journal-title":"Trans. AIME"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Lucia, A., Voskov, D., James, S.C., Zaydullin, R., and Henley, H. (2013, January 5\u20137). Fully compositional and thermal reservoir simulations efficiently compare EOR techniques. Proceedings of the SPE Canada Unconventional Resources Conference, Calgary, AB, Canada.","DOI":"10.2118\/167184-MS"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"3357","DOI":"10.1029\/94WR02046","article-title":"A comparison of Picard and Newton iteration in the numerical solution of multidimensional variably saturated flow problems","volume":"30","author":"Paniconi","year":"1994","journal-title":"Water Resour. Res."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1593","DOI":"10.1002\/nag.2400","article-title":"Accuracy and convergence properties of the fixed-stress iterative solution of two-way coupled poromechanics","volume":"39","author":"Castelletto","year":"2015","journal-title":"Int. J. Numer. Anal. Methods Geomech."},{"key":"ref_37","unstructured":"Younis, R.M. (2011). Modern Advances in Software and Solution Algorithms for Reservoir Simulation, Stanford University."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1016\/j.peva.2009.07.003","article-title":"Software performance simulation strategies for high-level embedded system design","volume":"67","author":"Wang","year":"2010","journal-title":"Perform. Eval."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"4341","DOI":"10.1007\/s11831-022-09739-2","article-title":"Linear solvers for reservoir simulation problems: An overview and recent developments","volume":"29","author":"Nardean","year":"2022","journal-title":"Arch. Comput. Methods Eng."},{"key":"ref_40","first-page":"171","article-title":"Reservoir simulation: Past, present, and future","volume":"9","author":"Watts","year":"1997","journal-title":"SPE Comput. Appl."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/S0377-0427(00)00422-2","article-title":"Automatic differentiation of algorithms","volume":"124","author":"Brown","year":"2000","journal-title":"J. Comput. Appl. Math."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Voskov, D.V., and Tchelepi, H.A. (2011, January 21\u201323). Compositional nonlinear solver based on trust regions of the flux function along key tie-lines. Proceedings of the SPE Reservoir Simulation Conference, The Woodlands, TX, USA.","DOI":"10.2118\/141743-MS"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1125","DOI":"10.2514\/3.13202","article-title":"Comparison of numerical and analytical Jacobians","volume":"34","author":"Vanden","year":"1996","journal-title":"AIAA J."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"107506","DOI":"10.1016\/j.petrol.2020.107506","article-title":"A novel linear solver for simulating highly heterogeneous black oil reservoirs","volume":"194","author":"Mohajeri","year":"2020","journal-title":"J. Pet. Sci. Eng."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Oberkampf, W.L., and Roy, C.J. (2010). Verification and Validation in Scientific Computing, Cambridge University Press.","DOI":"10.1017\/CBO9780511760396"},{"key":"ref_46","unstructured":"Khebzegga, O. (2020). Advanced Nonlinear Techniques for Compositional Reservoir Simulation, Stanford University."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Abd, A.S., Asif, A., and Abushaikha, A. (2024). Performance analysis of linearization schemes for modelling multi-phase flow in porous media. Sci. Rep., 14.","DOI":"10.1038\/s41598-024-66628-3"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Asif, A., Abd, A., and Abushaikha, A. (2024, January 2\u20135). A Residual-Accelerated Jacobian Method for Rapid Convergence in Reservoir Simulation. Proceedings of the ECMOR 2024\u2014European Association of Geoscientists & Engineers, Oslo, Norway.","DOI":"10.3997\/2214-4609.202437010"},{"key":"ref_49","unstructured":"Brooks, R., and Corey, A. (1964). Hydraulic properties of porous media. Civil Engineering Department, Colorado State University. Hydrology Paper No. 3."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"106673","DOI":"10.1016\/j.compfluid.2025.106673","article-title":"Adaptive fully implicit and thermodynamically consistent modeling of multiphase flow in porous media on three dimensional grids","volume":"298","author":"Sheng","year":"2025","journal-title":"Comput. Fluids"},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Iranshahr, A., Voskov, D., and Tchelepi, H.A. (2011, January 21\u201323). A negative-flash tie-simplex approach for multiphase reservoir simulation. Proceedings of the SPE Reservoir Simulation Conference, The Woodlands, TX, USA.","DOI":"10.2118\/141896-MS"},{"key":"ref_52","unstructured":"Li, Y. (2021). Robust and Accurate VT Flash Calculation and Efficient VT-Flash Based Compositional Flow Simulation. [Ph.D. Thesis, King Abdullah University of Science and Technology]."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0378-3812(82)85001-2","article-title":"The isothermal flash problem. Part I. Stability","volume":"9","author":"Michelsen","year":"1982","journal-title":"Fluid Phase Equilibria"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"363","DOI":"10.2118\/8284-PA","article-title":"An equation of state compositional model","volume":"20","author":"Coats","year":"1980","journal-title":"Soc. Pet. Eng. J."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1007\/s11242-011-9919-2","article-title":"An extended natural variable formulation for compositional simulation based on tie-line parameterization","volume":"92","author":"Voskov","year":"2012","journal-title":"Transp. Porous Media"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1989","DOI":"10.2118\/209233-PA","article-title":"Dissipation-based nonlinear solver for fully implicit compositional simulation","volume":"27","author":"Jiang","year":"2022","journal-title":"SPE J."},{"key":"ref_57","unstructured":"Chaabi, O., and Al-Kobaisi, M. (2025). Adaptive Nonlinear Elimination Preconditioning for Transport in Fractured Porous Media. arXiv."},{"key":"ref_58","unstructured":"Riseth, A.N. (2015). Nonlinear Solver Techniques in Reservoir Simulation: A Review, Oxford University Mathematical Institute. Technical Report."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"112006","DOI":"10.1016\/j.jcp.2023.112006","article-title":"Efficient dissipation-based nonlinear solver for multiphase flow in discrete fractured media","volume":"479","author":"Jiang","year":"2023","journal-title":"J. Comput. Phys."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1137\/080743627","article-title":"Introduction to automatic differentiation and MATLAB object-oriented programming","volume":"52","author":"Neidinger","year":"2010","journal-title":"SIAM Rev."},{"key":"ref_61","doi-asserted-by":"crossref","unstructured":"Xu, Z., and Okuno, R. (2015, January 23\u201325). Numerical simulation of three-hydrocarbon-phase flow with robust phase identification. Proceedings of the SPE Reservoir Simulation Conference, Houston, TX, USA.","DOI":"10.2118\/173202-MS"},{"key":"ref_62","unstructured":"Li, J. (2022). Sequential Fully Implicit Newton Method for Reservoir Simulation, Stanford University."},{"key":"ref_63","doi-asserted-by":"crossref","unstructured":"Griewank, A., and Walther, A. (2008). Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, Society for Industrial and Applied Mathematics.","DOI":"10.1137\/1.9780898717761"},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Jiang, J., and Wen, X.H. (2023, January 28\u201330). Smooth Formulation for Three-Phase Black-Oil Simulation with Superior Nonlinear Convergence. Proceedings of the SPE Reservoir Simulation Conference, Galveston, TX, USA.","DOI":"10.2118\/212261-MS"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"522","DOI":"10.2118\/182685-PA","article-title":"Adaptive Parameterization for Solving of Thermal\/Compositional Nonlinear Flow and Transport with Buoyancy","volume":"23","author":"Khait","year":"2018","journal-title":"SPE J."},{"key":"ref_66","unstructured":"Khait, M., and Voskov, D. (September, January 29). Operator-based linearization for non-isothermal multiphase compositional flow in porous media. Proceedings of the ECMOR XV-15th European Conference on the Mathematics of Oil Recovery, Amsterdam, The Netherlands."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/j.jcp.2017.02.041","article-title":"Operator-based linearization approach for modeling of multiphase multi-component flow in porous media","volume":"337","author":"Voskov","year":"2017","journal-title":"J. Comput. Phys."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"1684","DOI":"10.1002\/aic.13919","article-title":"Tie-simplex based compositional space parameterization: Continuity and generalization to multiphase systems","volume":"59","author":"Iranshahr","year":"2013","journal-title":"AIChE J."},{"key":"ref_69","first-page":"1","article-title":"Tie-simplex parametrization for operator-based linearization for non-isothermal multiphase compositional flow in porous","volume":"Volume 2018","author":"Khait","year":"2018","journal-title":"Proceedings of the ECMOR XVI-16th European Conference on the Mathematics of Oil Recovery"},{"key":"ref_70","doi-asserted-by":"crossref","unstructured":"Pour, K.M., and Voskov, D. (2020, January 14\u201317). Adaptive nonlinear solver for a discrete fracture model in operator-based linearization framework. Proceedings of the ECMOR XVII\u2014European Association of Geoscientists & Engineers, Online Event.","DOI":"10.3997\/2214-4609.202035094"},{"key":"ref_71","doi-asserted-by":"crossref","unstructured":"De Hoop, S., Voskov, D., and Bertotti, G. (2020, January 14\u201317). Studying the effects of heterogeneity on dissolution processes using operator based linearization and high-resolution lidar data. Proceedings of the ECMOR XVII\u2014European Association of Geoscientists & Engineers, Edinburgh, UK.","DOI":"10.3997\/2214-4609.202035184"},{"key":"ref_72","unstructured":"Abushaikha, A.S. (2013). Numerical Methods for Modelling Fluid Flow in Highly Heterogeneous and Fractured Reservoirs. [Ph.D. Thesis, Imperial College London]."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1007\/s11242-021-01585-3","article-title":"Modeling the effects of capillary pressure with the presence of full tensor permeability and discrete fracture models using the mimetic finite difference method","volume":"137","author":"Abd","year":"2021","journal-title":"Transp. Porous Media"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1007\/s10596-021-10096-5","article-title":"A fully-implicit parallel framework for complex reservoir simulation with mimetic finite difference discretization and operator-based linearization","volume":"26","author":"Li","year":"2021","journal-title":"Comput. Geosci."},{"key":"ref_75","first-page":"1","article-title":"A Novel and Efficient Preconditioner for Solving Lagrange Multipliers-Based Discretization Schemes for Reservoir Simulations","volume":"2020","author":"Nardean","year":"2020","journal-title":"ECMOR XVII"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"109194","DOI":"10.1016\/j.jcp.2019.109194","article-title":"A fully implicit mimetic finite difference scheme for general purpose subsurface reservoir simulation with full tensor permeability","volume":"406","author":"Abushaikha","year":"2020","journal-title":"J. Comput. Phys."},{"key":"ref_77","doi-asserted-by":"crossref","unstructured":"Zhang, N., and Abushaikha, A.S. (2019, January 3\u20136). An efficient mimetic finite difference method for multiphase flow in fractured reservoirs. Proceedings of the SPE Europec Featured at EAGE Conference and Exhibition, London, UK.","DOI":"10.2118\/195512-MS"},{"key":"ref_78","doi-asserted-by":"crossref","unstructured":"Zhang, N., and Abushaikha, A.S. (2019, January 18). Fully Implicit Reservoir Simulation Using Mimetic Finite Difference Method in Fractured Carbonate Reservoirs. Proceedings of the SPE Reservoir Characterisation and Simulation Conference and Exhibition, Abu Dhabi, United Arab Emirates.","DOI":"10.2118\/196711-MS"},{"key":"ref_79","doi-asserted-by":"crossref","unstructured":"Hjeij, D., and Abushaikha, A. (2019, January 18). Comparing Advanced Discretization Methods for Complex Hydrocarbon Reservoirs. Proceedings of the SPE Reservoir Characterisation and Simulation Conference and Exhibition, Abu Dhabi, United Arab Emirates.","DOI":"10.2118\/196727-MS"},{"key":"ref_80","doi-asserted-by":"crossref","unstructured":"Hjeij, D., and Abushaikha, A. (2019, January 5). An Investigation of the Performance of the Mimetic Finite Difference Scheme for Modelling Fluid Flow in Anisotropic Hydrocarbon Reservoirs. Proceedings of the SPE Europec Featured at EAGE Conference and Exhibition, London, UK.","DOI":"10.2118\/195496-MS"},{"key":"ref_81","doi-asserted-by":"crossref","unstructured":"Abushaikha, A.S., Voskov, D.V., and Tchelepi, H.A. (2017, January 21). Fully Implicit Mixed Hybrid Finite-Element Formulation for General-Purpose Compositional Reservoir Simulation. Proceedings of the SPE Reservoir Simulation Conference, Montgomery, TX, USA.","DOI":"10.2118\/182697-MS"},{"key":"ref_82","first-page":"1748","article-title":"Newton raphson method","volume":"6","author":"Akram","year":"2015","journal-title":"Int. J. Sci. Eng. Res."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1137\/1037125","article-title":"Historical development of the Newton\u2013Raphson method","volume":"37","author":"Ypma","year":"1995","journal-title":"SIAM Rev."},{"key":"ref_84","unstructured":"Ma, S., and Saad, Y. (1994). Distributed ILU (0) and SOR Preconditioners for Unstructured Sparse Linear Systems, University of Minnesota. Citeseer."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1006\/jcph.2002.7176","article-title":"Preconditioning techniques for large linear systems: A survey","volume":"182","author":"Benzi","year":"2002","journal-title":"J. Comput. Phys."},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0024-3795(83)90091-5","article-title":"A note on MGR methods","volume":"49","author":"Ries","year":"1983","journal-title":"Linear Algebra Its Appl."},{"key":"ref_87","doi-asserted-by":"crossref","unstructured":"Wu, W., Li, X., He, L., and Zhang, D. (2014, January 16\u201319). Accelerating the iterative linear solver for reservoir simulation on multicore architectures. Proceedings of the 2014 20th IEEE International Conference on Parallel and Distributed Systems (ICPADS), Hsinchu, Taiwan.","DOI":"10.1109\/PADSW.2014.7097817"}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/13\/8\/191\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:26:04Z","timestamp":1760034364000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/13\/8\/191"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,8]]},"references-count":87,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,8]]}},"alternative-id":["computation13080191"],"URL":"https:\/\/doi.org\/10.3390\/computation13080191","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2025,8,8]]}}}