×

General template units for the finite volume method in box-shaped domains. (English) Zbl 1371.65091


MSC:

65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
65Y15 Packaged methods for numerical algorithms
76S05 Flows in porous media; filtration; seepage
76M12 Finite volume methods applied to problems in fluid mechanics
76R10 Free convection
76R05 Forced convection
76T10 Liquid-gas two-phase flows, bubbly flows
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] A. Al-Huthali and A. Datta-Gupta. 2004. Streamline simulation of counter-current imbibition in naturally fractured reservoirs. Journal of Petroleum Science and Engineering 43, 271–300.
[2] M. Allen, I. Herrera, and G. Pinder. 1998. Numerical Modelling in Science and Engineering. John Wiley & Sons, New York, NY. · Zbl 0636.65128
[3] M. H. Austern. 1999. Generic Programming and the STL: Using and Extending the C++ Standard Template Library. Addison-Wesley, New York, NY.
[4] S. Balay, J. Brown, K. Buschelman, W. D. Gropp, D. Kaushik, M. G. Knepley, L. C. McInnes, B. F. Smith, and H. Zhang. 2011. PETSc Web page. Retrieved July 16, 2016 from http://www.mcs.anl.gov/petsc.
[5] W. Bangerth, R. Hartmann, and G. Kanschat. 2007. deal.II– A general–purpose object–oriented finite element library. ACM Transactions on Mathematical Software 33, 4. · Zbl 1365.65248
[6] J. J. Barton and L. R. Nackman. 1994. Scientifc and Engineering C++. Addison–Wesley, New York, NY.
[7] R. Bastiaans, C. Rindt, F. Nieuwstadt, and A. van Steenhoven. 2000. Direct and large–eddy simulation of the transitional of two– and three–dimensional plane plumes in a confined enclosure. International Journal of Heat and Mass Transfer 43, 2375–2393. · Zbl 0991.76080
[8] E. Bertolazzi and G. Manzini. 2002. Algorithm: P2MESH: Generic object-oriented interface between 2-D unstructured meshes and FEM/FVM-based PDE solvers. ACM Transactions on Mathematical Software 28, 1, 101–131. · Zbl 1070.65568
[9] D. L. Brown, W. D. Henshaw, and D. J. Quinlan. 1997. Overture: An object oriented framework for solving partial differential equations. In Lecture Notes in Computer Science. Vol. 1343. Springer, Berlin. Retrieved July 16, 2016 from https://computation.llnl.gov/casc/Overture/.
[10] S. Buckley and M. Leverett. 1942. Mechanism of fluid displacement in sands. Transactions of the AIME 146, 107–116.
[11] P. Castillo, R. Rieben, and D. White. 2005. FEMSTER: An object-oriented class library of high-order discrete differential forms. ACM Transactions on Mathematical Software 31, 4, 425–457. http://www.swmath.org/software/275. · Zbl 1136.78330
[12] Z. Chen, G. Huan, and Y. Ma. 2006. Computational Methods for Multiphase Flows in Porous Media. SIAM, Philadelphia, PA. · Zbl 1092.76001
[13] J. O. Coplien. 1995. Curiously recurring template patterns. C++ Report, 24–27.
[14] A. Corey. 1954. The interrelation between gas and oil relative permeabilities. Producers Monthly 19, 1, 3841.
[15] CUSP. Library of generic parallel algorithms for sparse matrix and graph computations. Retrieved July 16, 2016 from http://code.google.com/p/cusp-library/.
[16] E. David. 1993. Modélisation des écoulements compressibles et hypersoniques: une approche instantionnaire. Ph.D. dissertation. National Polytechnic Institute, Grenoble, France.
[17] L. de la Cruz. TUNAM: Template units for numerical applications and modeling. Retrieved July 16, 2016 from http://code.google.com/p/tunam/.
[18] L. M. de la Cruz. 2005. Parallel computing of balance equations in turbulent flow. Ph.D. dissertation. IIMAS, UNAM, Mexico. In Spanish. Retrieved July 16, 2016 from http://bc.unam.mx/index-alterno.html.
[19] Eigen. C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms. Retrieved July 16, 2016 from http://eigen.tuxfamily.org/.
[20] FLENS. Flexible library for efficient numerical solutions. Retrieved July 16, 2016 from http://flens.sourceforge.net/.
[21] M. Hatakeyama, M. Watanabe, and T. Suzuki. 1998. Object-oriented fluid flow simulation system. Computers & Fluids 27, 5–6, 581–597. · Zbl 0955.76078
[22] T. Hayase, J. A. C. Humphrey, and R. Greif. 1992. A consistently formulated QUICK scheme for fast and stable convergence using finite-volume iterative calculation procedures. Journal of Computational Physics 98, 1, 108–118. · Zbl 0743.76054
[23] I. Herrera and G. S. Herrera. 2011. Unified formulation of enhanced oil-recovery methods. Geofisica Internacional 50, 1.
[24] I. Herrera and G. Pinder. 2012. Mathematical Modeling in Science and Engineering: An Axiomatic Approach. John Wiley & Sons, New York, NY.
[25] P. S. Kholsa and S. G. Rubin. 1974. A diagonal dominant second-order accurate implicit scheme. Computers and Fluids 2, 207–209. · Zbl 0335.76009
[26] B. S. Kirk, J. W. Peterson, R. H. Stogner, and G. F. Carey. 2006. libMesh: A C++ Library for Parallel Adaptive Mesh Refinement/Coarsening Simulations. Engineering with Computers 22, 3–4, 237–254. http://dx.doi.org/10.1007/s00366-006-0049-3. · Zbl 05192775
[27] D. B. Kirk and W. W. Hwu. 2010. Programming Massively Parallel Processors: A Hands-on Approach. Morgan Kaufmann, Burlington, MA.
[28] D. Kuzmin, R. Löhner, and S. Turek. 2012. Flux–Corrected Transport: Principles, Algorithms and Applications. 2nd ed. Scientific Computation. Springer, New York, NY.
[29] S. Lamine and M. G. Edwards. 2010. Higher order multidimensional upwind convection schemes for flow in porous media on structured and unstructured quadrilateral grids. SIAM Journal on Scientific Computing 32, 3, 1119–1139. · Zbl 1217.35010
[30] H. P. Langtangen and O. Munthe. 2001. Solving systems of partial differential equations using object-oriented programming techniques with coupled heat and fluid flow as example. ACM Transactions on Mathematical Software 27, 1, 1–26. · Zbl 1070.65561
[31] B. P. Leonard. 1979. A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comp. Meth. in App. Mech. and Engineering 19, 59–98. · Zbl 0423.76070
[32] M. Lesieur and O. Métais. 1996. New trends in large-eddy simulations of turbulence. Annual Review of Fluid Mechanics 28, 45–82.
[33] R. J. Leveque. 2002. Finite Volume Methods for Hyperbolic Problems. Cambridge University Press, New York, NY. · Zbl 1010.65040
[34] A. Lipchin and R. A. Brown. 1999. Comparison of three turbulence models for simulation of melt convection in Czochralski crystal growth of silicon. Journal of Crystal Growth 205, 1–2, 71–91.
[35] J.-L. Liu, I.-J. Lin, M.-Z. Shih, R.-C. Chen, and M.-C. Hsieh. 1996. Object-oriented programming of adaptive finite element and finite volume methods. Applied Numerical Mathematics 21, 4, 439–467. · Zbl 0865.65079
[36] A. Logg and G. N. Wells. 2010. DOLFIN: Automated finite element computing. ACM Transactions on Mathematical Software 37, 2. http://fenicsproject.org/. · Zbl 1364.65254
[37] MTL4. Matrix template library 4. Retrieved July 16, 2016 from http://www.simunova.com/de/mtl4.
[38] N. Myers. 1995. Traits: A new and useful template technique. C++ Report.
[39] J. Nie, D. Hopkins, Y. Chen, and H. Hsieh. 2010. Development of an object-oriented finite element program with adaptive mesh refinement for multi-physics applications. Advances in Engineering Software 41, 4, 569–579. · Zbl 1406.74640
[40] NIST. FiPy: A finite volume PDE solver using Python. Retrieved July 16, 2016 from http://www.ctcms.nist.gov/fipy/.
[41] S. Norris. 2000. A parallel Navier–Stokes solver for natural convection and free surface flow. Ph.D. dissertation. Department of Mechanical Engineering, University of Sydney, Sydney, Australia.
[42] S. V. Patankar. 1980. Numerical Heat Transfer and Fluid Flow. McGraw–Hill, New York, NY. · Zbl 0521.76003
[43] L. Pesch, A. Bell, H. Sollie, V. R. Ambati, O. Bokhove, and J. J. V. D. Vegt. 2007. hpGEM – A software framework for discontinuous Galerkin finite element methods. ACM Transactions on Mathematical Software 33, 4. http://www.hpgem.org. · Zbl 1365.65261
[44] Seldon. C++ library for linear algebra. Retrieved July 16, 2016 from http://seldon.sourceforge.net/.
[45] Y. Tian and T. Karayiannis. 2000a. Low turbulence natural convection in an air filled square cavity, Part I: The thermal and fluid flow fields. International Journal of Heat and Mass Transfer 43, 849–866. · Zbl 1065.76511
[46] Y. Tian and T. Karayiannis. 2000b. Low turbulence natural convection in an air filled square cavity, Part II: The thermal and fluid flow fields. International Journal of Heat and Mass Transfer 43, 867–884. · Zbl 1065.76511
[47] uBlas. Basic linear algebra library. Retrieved July 16, 2016 from http://www.boost.org/.
[48] J. P. Van Doormaal and G. D Raithby. 1984. Enhancements of the simple method for predicting incompressible fluid flows. Numerical Heat Transfer 7, 147–163. · Zbl 0553.76005
[49] D. Vandevoorde and N. M. Josuttis. 2003. C++ Templates. Addison-Wesley, New York, NY.
[50] T. Veldhuizen. Blitz++: Object-oriented library for scientific computing. Retrieved July 16, 2016 from http://sourceforge.net/projects/blitz/.
[51] T. L. Veldhuizen. 1995a. Expression templates. C++ Report 7, 5, 26–31. Reprinted in C++ Gems, ed. Stanley Lippman.
[52] T. L. Veldhuizen. 1995b. Using C++ template metaprograms. C++ Report 7, 4, 36–43. Reprinted in C++ Gems, ed. Stanley Lippman.
[53] T. L. Veldhuizen. 1998. Arrays in Blitz++. In Lecture Notes in Computer Science. Vol. 1505. Springer, Berlin.
[54] H. K. Versteeg and W. Malalasekera. 1995. An introduction to computation of fluid dynamics. The finite volume method. Longman Scientific and Technical, Harlow, UK.
[55] H. Weller, G. Tabor, H. Jasak, and C. Fureby. 1998. A tensorial approach to CFD using object orientated techniques. Computers in Physics 12, 6, 620–631.
[56] J. Xaman, G. Alvarez, L. Lira, and C. Estrada. 2005. Numerical study of heat transfer by laminar and turbulent natural convection in tall cavities of facade elements. Energy and Buildings 37, 7, 787–794.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.