Parallel Domain Decomposition of a FEM-based Tool for Numerical Modelling Mineral Slurry-like Flows

References

• Baha Abulnaga, P. E. 2002. Slurry Systems Handbook. New York: McGraw-Hill Education.
   Google Scholar
• Amritkar, A., S. Deb, and D. Tafti. 2014. “Efficient Parallel CFD-DEM Simulations Using Openmp.” Journal of Computational Physics 256: 501–519.
   Web of Science ®Google Scholar
• Balay, S., S. Abhyankar, M. Adams, J. Brown, P. Brune, K. Buschelman, L. Dalcin, et al. 2019. PETSc Users Manual. Lemont, IL: Argonne National Laboratory.
   Google Scholar
• Celis, C., A. Antoniou, J. Cuisano, A. Pillihuaman, and d. Maza. 2021. “Experimental Characterization of Chalcopyrite Ball Mill Grinding Processes in Batch and Continuous Flow Processing Modes to Reduce Energy Consumption.” Journal of Materials Research and Technology 15, 5428–5444.
   Google Scholar
• Chapra, S. C., and R. P. Canale. 2011. Numerical Methods for Engineers. Vol. 1221. New York: Mcgraw-Hill.
   Google Scholar
• Chen, R., Y. Wu, Z. Yan, Y. Zhao, and X.-C. Cai. 2014. “A Parallel Domain Decomposition Method for 3D Unsteady Incompressible Flows at High Reynolds Number.” Journal of Scientific Computing 58 (2): 275–289.
   Web of Science ®Google Scholar
• Chhabra, R. P.. 2010. “Non-Newtonian Fluids: An Introduction.” In Rheology of Complex Fluids, edited by J. Murali Krishnan, A. P. Deshpande, and P. B. Sunil Kumar, 3–34. New York, NY: Springer.
   Google Scholar
• Chhabra, R., A. Soares, and J. Ferreira. 2004. “Steady Non–Newtonian Flow Past a Circular Cylinder: A Numerical Study.” Acta Mechanica 172 (1–2): 1–16.
   Web of Science ®Google Scholar
• Dryja, M., and O. Widlund. 1987. An additive Variant of the Schawrz Alternating Method for the Case of Many Subregions. Computer Science Technical Report #339. Ultracomputer Research Laboratory, Univ., Courant Inst. of Mathematical. https://ia800704.us.archive.org/1/items/additivevarianto00dryj/additivevarianto00dryj_bw.pdf [Verified 15 March 2022]
   Google Scholar
• Erhel, J., K. Burrage, and B. Pohl. 1996. “Restarted GMRES Preconditioned by Deflation.” Journal of Computational and Applied Mathematics 69 (2): 303–318.
   Web of Science ®Google Scholar
• Farhat, C.. 1988. “A Simple and Efficient Automatic Fem Domain Decomposer.” Computers & Structures 28 (5): 579–602.
   Web of Science ®Google Scholar
• Ferziger, J. H., M. Perić, and R. L. Street. 2002. Computational Methods for Fluid Dynamics. Vol. 3. Berlin: Springer.
   Google Scholar
• Gresho, P. M., and R. L. Sani. 1998. Incompressible Flow and the Finite Element Method. Volume 1: Advection-Diffusion and Isothermal Laminar Flow. New York, NY: John Wiley and Sons, Inc..
   Google Scholar
• Gropp, W., W. D. Gropp, E. Lusk, A. Skjellum, and A. D. F. E. E. Lusk. 1999. Using MPI: Portable Parallel Programming with the Message-Passing Interface. Vol. 1. Cambridge: MIT press.
   Google Scholar
• Houzeaux, G., R. Borrell, J. Cajas, and M. Vázquez. 2018. “Extension of the Parallel Sparse Matrix Vector Product (SpMV) for the Implicit Coupling of Pdes on Non-Matching Meshes.” Computers & Fluids 173: 216–225.
   Web of Science ®Google Scholar
• Houzeaux, G., J. Cajas, M. Discacciati, B. Eguzkitza, A. Gargallo-Peiró, M. Rivero, and M. Vázquez. 2017. “Domain Decomposition Methods for Domain Composition Purpose: Chimera, Overset, Gluing and Sliding Mesh Methods.” Archives of Computational Methods in Engineering 24 (4): 1033–1070.
   Web of Science ®Google Scholar
• Houzeaux, G., and R. Codina. 2001. “Transmission Conditions with Constraints in Finite Element Domain Decomposition Methods for Flow Problems.” Communications in Numerical Methods in Engineering 17 (3): 179–190.
   Web of Science ®Google Scholar
• Houzeaux, G., and R. Codina. 2003. “A Chimera Method Based on a Dirichlet/Neumann (Robin) Coupling for the Navier–Stokes Equations.” Computer Methods in Applied Mechanics and Engineering 192 (31–32): 3343–3377.
   Web of Science ®Google Scholar
• Jacob, F., and B. Ted. 2007. A First Course in Finite Elements. Chichester: Wiley.
   Google Scholar
• Japhet, C., M. Kern, and J. E. Roberts. 2017. “Space–Time Domain Decomposition for Advection–Diffusion Problems in Mixed Formulations.” Mathematics and Computers in Simulation 137: 366–389.
   Web of Science ®Google Scholar
• Jouybari, N. F., B. Engberg, and J. Persson. 2020. “Large Eddy Simulation of Turbulent Pulp Flow in a Channel.” Journal of Non-Newtonian Fluid Mechanics 285: 104409.
   Google Scholar
• Karniadakis, G., G. E. Karniadakis, and R. M. Kirby. 2003. II: Parallel Scientific Computing in C++ and MPI: A Seamless Approach to Parallel Algorithms and Their Implementation. Vol. 1. New York: Cambridge University Press.
   Google Scholar
• Karypis, G., K. Schloegel, and V. Kumar. 1997. Parmetis: Parallel Graph Partitioning and Sparse Matrix Ordering Library. TR 97-060. Department of Computer Science and Engineering, University of Minnesota, Minneapolis, US. https://conservancy.umn.edu/bitstream/handle/11299/215345/1997-060.pdf?sequence=1 [Verified 17 October 2021]
   Google Scholar
• Lavrov, A.. 2015. “Flow of Truncated Power-Law Fluid Between Parallel Walls for Hydraulic Fracturing Applications.” Journal of Non-Newtonian Fluid Mechanics 223: 141–146.
   Web of Science ®Google Scholar
• Martin, V.. 2009. “Schwarz Waveform Relaxation Algorithms for the Linear Viscous Equatorial Shallow Water Equations.” SIAM Journal on Scientific Computing 31 (5): 3595–3625.
   Web of Science ®Google Scholar
• Michaelides, E., C. T. Crowe, and J. D. Schwarzkopf. 2016. Multiphase Flow Handbook. Boca Raton: CRC Press.
   Google Scholar
• Peralta, S., J. Cordova, C. Celis, and D. Maza. 2020a. “Development of an Object-Oriented Programming Tool Based on Fem for Numerical Simulation of Mineral-Slurry Transport.” In International Conference on Computational Science, 163–177. Lecture Notes in Computer Science, 12143 vols. Cham: Springer. https://doi.org/10.1007/978-3-030-50436-6_12
   Google Scholar
• Peralta, S., J. Córdova, C. Celis, and D. Maza. 2020b. “Numerical Modelling of Mineral-Slurry Like Flows in a 3D Lid-Driven Cavity Using a Finite Element Method Based Tool.” In Proceedings of the ASME 2020 International Mechanical Engineering Congress and Exposition. 10 vols: Fluids Engineering. Virtual, Online. November 16-19, 2020. V010T10A023. ASME. https://doi.org/10.1115/IMECE2020-24130
   Google Scholar
• Pritchard, P. J., and J. W. Mitchell. 2016. Fox and McDonald's Introduction to Fluid Mechanics. Kendallville: John Wiley & Sons.
   Google Scholar
• Raju, M. P., and S. Khaitan. “Domain Decomposition Based High Performance Parallel Computing.” arXiv preprint arXiv:0911.0910.
   Google Scholar
• Reddy, J. N., and D. K. Gartling. 2010. The Finite Element Method in Heat Transfer and Fluid Dynamics. Boca Raton: CRC Press.
   Google Scholar
• Saad, Y.. 2003. Iterative Methods for Sparse Linear Systems. Philadelphia: SIAM.
   Google Scholar
• Saad, Y., and M. H. Schultz. 1986. “GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems.” SIAM Journal on Scientific and Statistical Computing 7 (3): 856–869.
   Web of Science ®Google Scholar
• Shiu, W.-S., F.-N. Hwang, and X.-C. Cai. 2015. “Parallel Domain Decomposition Method for Finite Element Approximation of 3D Steady State Non-Newtonian Fluids.” International Journal for Numerical Methods in Fluids 78 (8): 502–520.
   Web of Science ®Google Scholar
• Tang, H., R. Haynes, and G. Houzeaux. 2021. “A Review of Domain Decomposition Methods for Simulation of Fluid Flows: Concepts, Algorithms, and Applications.” Archives of Computational Methods in Engineering 28 (3): 841–873.
   Web of Science ®Google Scholar
• Versteeg, H. K., and W. Malalasekera. 2007. An Introduction to Computational Fluid Dynamics: The Finite Volume Method. Glasgow: Pearson education.
   Google Scholar
• Wang, C.-H., and J.-R. Ho. 2011. “A Lattice Boltzmann Approach for the Non-Newtonian Effect in the Blood Flow.” Computers & Mathematics with Applications 62 (1): 75–86.
   Web of Science ®Google Scholar
• Wu, D., W. Chen, D. Glowinski, and C. Wheeler. 2020. “Modelling Mineral Slurries Using Coupled Discrete Element Method and Smoothed Particle Hydrodynamics.” Powder Technology 364: 553–561.
   Web of Science ®Google Scholar
• Wu, J., L. Graham, S. Wang, and R. Parthasarathy. 2010. “Energy Efficient Slurry Holding and Transport.” Minerals Engineering 23 (9): 705–712.
   Web of Science ®Google Scholar
• Xu, G., K. D. Luxbacher, S. Ragab, J. Xu, and X. Ding. 2017. “Computational Fluid Dynamics Applied to Mining Engineering: A Review.” International Journal of Mining, Reclamation and Environment 31 (4): 251–275.
   Web of Science ®Google Scholar