Fully implicit method for coupling multiblock meshes with nonmatching interface grids

References

• D. You, R. Mittal, M. Wang, and P. Moin, Large-Eddy Simulation of a Rotor Tip-clearance Flow, AIAA Paper 2002–0981, 2002.
   Google Scholar
• R. Mittal, S. Venkatasubramanian, and F. M. Najjar, Large Eddy Simulation of Flow through a Low-Pressure Turbine, AIAA Paper 2001–2560, 2001.
   Google Scholar
• M. Wang and P. Moin, Computation of Trailing-edge Flow and Noise Using Large-Eddy Simulation, AIAA J., vol. 38, pp. 2201–2209, 2000.
   Google Scholar
• C. Erath and D. Praetorius, A Posteriori Error Estimate and Adaptive Mesh Refinement for the Cell-centered Finite Volume Method for Elliptic Boundary Value Problems, SIAM J. Numer. Anal., vol. 47, no. 1, pp. 109–135, 2008.
   Web of Science ®Google Scholar
• M. A. Martins, R. M. Valle, L. S. Oliveira, and D. Burgarelli, Error Estimation and Adaptivity for Finite Volume Methods on Unstructured Triangular Meshes: Elliptic Heat Transfer Problems, Numer. Heat Transfer Part B Fundam., vol. 42, pp. 461–483, 2002.
   Web of Science ®Google Scholar
• A. Rouboa and E. Monteiro, Heat Transfer in Multi-block Grid During Solidification: Performance of Finite Differences and Finite Volume Methods, J. Mater. Process. Technol., vol. 204, pp. 451–458, 2008.
   Web of Science ®Google Scholar
• Y. Guowei, K. Masahiro, and O. Shigeru, Multiblock Navier–Stokes Solver for Wing/Fuselage Transport Aircraft, JSME Int. J. Ser. B Fluids Therm. Eng., vol. 45, no. 1, pp. 85–90, 2002.
   Web of Science ®Google Scholar
• C. W. Lin, G. D. Smith, and S. C. Fisher, Application of a Multiblock Grid Generation Approach to Ship Configuration, 3rd International Conference on Numerical Grid Generation in CFD, Spain, June 1991.
   Google Scholar
• R. L. Meakin, Composite Overset Structured Grids, in Thompson, Soni, and Weatherill (eds.), Handbook of Grid Generation, chap. 11, CRC Press, 1999.
   Google Scholar
• Y. Zheng and M. S. Liou, A Novel Approach of Three-dimensional Hybrid Grid Methodology: Part 1. Grid Generation, Comput. Methods Appl. Mech. Eng., vol. 192, pp. 4147–4171, 2003.
   Web of Science ®Google Scholar
• L. Saas, I. Faille, F. Nataf, and F. Willien, Finite Volume Methods for Domain Decomposition on Non-matching Grids with Arbitrary Interface Conditions, SIAM J. Numer. Anal., vol. 43, no. 2, pp. 860–890, 2005.
   Web of Science ®Google Scholar
• R. Eymard and R. Herbin, A New Collocated Finite Volume Scheme for the Incompressible Navier–Stokes Equations on General Non Matching Grids, C. R. Acad. Sci. Ser. I Math., vol. 344, pp. 659–662, 2007.
   Google Scholar
• E. Aulisa, S. Manservisi, and P. Seshaiyer, A Computational Multilevel Approach for Solving 2D Navier–Stokes Equations over Non-matching Grids, Comput. Methods Appl. Mech. Eng., vol. 195, pp. 4604–4616, 2006.
   Web of Science ®Google Scholar
• O. Steinbach, A Natural Domain Decomposition Method with Non-matching Grids, Appl. Numer. Math., vol. 54, pp. 362–377, 2005.
   Web of Science ®Google Scholar
• L. Chang and G. Yuan, Cell-centered Finite Volume Methods with Flexible Stencils for Diffusion Equations on General Nonconforming Meshes, Comput. Methods Appl. Mech. Eng., vol. 198, pp. 1638–1646, 2009.
   Web of Science ®Google Scholar
• Z. Lilek, S. Muzaferija, M. Peric, and V. Seidl, An Implicit Finite Volume Method Using Non-matching Blocks of Structured Grid, Numer. Heat Transfer Part B Fundam., vol. 32, no. 4, pp. 385–401, 1997.
   Web of Science ®Google Scholar
• C. Romé and S. Glockner, An Implicit Multiblock Coupling for the Incompressible Navier–Stokes Equations, Int. J. Numer. Methods Fluids, vol. 47, pp. 1261–1267, 2005.
   Web of Science ®Google Scholar
• A. Pantano and R. C. Averill, A Penalty-based Interface Technology for Coupling Independently Modeled 3D Finite Element Meshes, Finite Elem. Anal. Des., vol. 43, pp. 271–286, 2007.
   Web of Science ®Google Scholar
• A. D. de Boer, A. H. van Zuijlen, and H. Bijl, Review of Coupling Methods for Non-matching Meshes, Comput. Methods Appl. Mech. Eng., vol. 196, pp. 1515–1525, 2007.
   Web of Science ®Google Scholar
• M. J. Smith, C. E. S. Cesnik, and D. H. Hodges, Evaluation of Some Data Transfer Algorithms for Noncontiguous Meshes, J. Aerosp. Eng., vol. 13, no. 2, pp. 52–58, 2000.
   Web of Science ®Google Scholar
• M. Darbandi and A. Naderi, Multiblok Hybrid Grid Finite Volume Method to Solve Flow in Irregular Geometries, Comput. Methods Appl. Mech. Eng., vol. 196, pp. 321–336, 2006.
   Web of Science ®Google Scholar
• S. V. Patankar, A Calculation Procedure for Two Dimensional Elliptic Situations, Numer. Heat Transfer, vol. 4, no. 4, pp. 409–425, 1981.
   Google Scholar
• S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, NY, 1980.
   Google Scholar
• S. V. Patankar, and D. B. Spalding, A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-dimensional Parabolic Flows, Int. J. Heat Mass Transfer, vol. 15, no. 10, pp. 1787–1806, 1972.
   Web of Science ®Google Scholar
• M. Darwish, D. Asmar, and F. Moukalled, A Comparative Assessment within a Multigrid Environment of Segregated Pressure-based Algorithms for Fluid Flow at all Speeds, Numer. Heat Transfer Part B Fundam., vol. 45, pp. 49–74, 2004.
   Web of Science ®Google Scholar
• F. Moukalled and M. Darwish, A High-resolution Pressure-based Algorithm for Fluid Flow at All Speeds, J. Comput. Phys., vol. 168, no.1, pp. 101–133, 2001.
   Web of Science ®Google Scholar
• F. Moukalled and M. Darwish, A Unified Formulation of the Segregated Class of Algorithms for Fluid Flow at All Speeds, Numer. Heat Transfer Part B Fundam., vol. 37, no 1, pp. 103–139, 2000.
   Web of Science ®Google Scholar
• F. Moukalled, L. Mangani, and M. Darwish, The Finite Volume Method in Computational Fluid Dynamics: An Advanced Introduction with OpenFOAM® and Matlab®, Springer International Publishing, Switzerland, 2015.
   Google Scholar
• F. Moukalled and M. Darwish, Pressure Based Algorithms for Single and Multifluid Flows, in W. J. Minkowycz E. M. Sparrow, and J. Y. Murthy (eds.), Handbook of Numerical Heat Transfer, 2nd ed., pp. 325–367, Wiley, 2006.
   Google Scholar
• C. M. Rhie and W. L. Chow, Numerical Study of The Turbulent Flow Past An Airfoil with Trailing Edge Separation, AIAA J., vol. 21, pp. 1525–1532, 1983.
   Google Scholar
• A. Carmona, O. Lehmkuhl, C. D. Perez-Segarra, and A. Oliva, Numerical Analysis of the Transpose Diffusive Term for Viscoplastic-type Non-Newtonian Fluid Flows using a Collocated Variable Arrangement, Numer. Heat Transfer Part B Fundam., vol. 67, no. 5, pp. 410–436, 2015.
   Web of Science ®Google Scholar
• P. Roy, N. K. Anand, and D. Donzis, A Parallel Multigrid Finite-volume Solver on a Collocated Grid for Incompressible Navier–Stokes Equations, Numer. Heat Transfer Part B Fundam., vol. 67, no. 5, pp. 376–409, 2015.
   Web of Science ®Google Scholar
• D. K. Kolmogorov, W. Z. Shen, N. N. Sorensen, and J. N. Sorensen, Fully Consistent Simple-like Algorithms on Collocated Grids, Numer. Heat Transfer Part B Fundam., vol. 67, no. 2, pp. 101–123, 2015.
   Web of Science ®Google Scholar
• F. Wang, W. Zhang, and Y. Li, Fourrier Analysis of the Effect of Momentum Interpolation on the SIMPLE Series Formulated on a Collocated Grid, Numer. Heat Transfer Part B Fundam., vol. 64, no. 1, pp. 48–70, 2013.
   Web of Science ®Google Scholar
• L. Bu, J. Zhao, and K. J. Tseng, Study on Momentum Interpolation Methods with Curvilinear Collocated Grids in Single-phase and Two-phase Flows, Numer. Heat Transfer Part B Fundam., vol. 61, no. 4, pp. 298–310, 2012.
   Web of Science ®Google Scholar
• M. Darwish, A. Abdel Aziz, and F. Moukalled, A Coupled Pressure-based Finite Volume Solver for Incompressible Two-phase Flow, Numer. Heat Transfer Part B Fundam., vol. 67, no. 1, pp. 47–74, 2015.
   Web of Science ®Google Scholar
• M. Darwish and F. Moukalled, A Fully Coupled Navier–Stokes Solver for Fluid Flow at All Speeds,” Numer. Heat Transfer Part B Fundam., vol. 45, pp. 410–444, 2014.
   Web of Science ®Google Scholar
• F. Moukalled, A. Abdel Aziz, and M. Darwish, Performance Comparison of the NWF and DC Methods for Implementing High-resolution Schemes in a Fully Coupled Incompressible Flow Solver, Appl. Math. Comput., vol. 217, no. 11, pp. 5041–5054, 2011.
   Web of Science ®Google Scholar
• M. Darwish, I. Sraj, and F. Moukalled, A Coupled Finite Volume Solver for the Solution of Incompressible Flows on Unstructured Grids, J. Comput. Phys., vol. 28, no. 1, pp. 180–201, 2009.
   Web of Science ®Google Scholar
• M. Darwish, I. Sraj, and F. Moukalled, A Coupled Incompressible Flow Solver on Structured Grids, Numer. Heat Transfer Part B Fundam., vol. 52, pp. 353–371, 2007.
   Web of Science ®Google Scholar
• F. Moukalled, and M. Darwish, New Bounded Skew Central Difference Scheme, Part I: Formulation and Testing, Numer. Heat Transfer, Part B Fundam., vol. 31, pp. 91–110, 1997.
   Web of Science ®Google Scholar