An implicit implementation of the characteristic boundary condition in a fully coupled pressure-based flow solver

References

• 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 Transf., vol. 15, no. 10, pp. 1787–1806, 1972. DOI: 10.1016/0017-9310(72)90054-3.
   Web of Science ®Google Scholar
• J. P. Van Doormaal and G. D. Raithby, “Enhancement of the SIMPLE method for predicting incompressible fluid flows,” Numer. Heat. Tr. B-Fund., vol. 7, no. 2, pp. 147–163, 1984. DOI: 10.1080/01495728408961817.
   Web of Science ®Google Scholar
• S. Acharya and F. Moukalled, “Improvements to incompressible flow calculation on a non-staggered curvilinear grid,” Numer. Heat. Tr. B-Fund., vol. 15, no. 2, pp. 131–152, 1989. DOI: 10.1080/10407798908944897.
   Web of Science ®Google Scholar
• S. V. Patankar, Numerical Heat Transfer and Fluid Flow. New York, NY: Hemisphere Publishing Corporation, 1980.
   Google Scholar
• A. Ashrafizadeh, B. Alinia and P. Mayeli, “A new co-located pressure-based discretization method for the numerical solution of incompressible Navier-Stokes equations,” Numer. Heat. Tr. B-Fund., vol. 67, no. 6, pp. 563–589, 2015. DOI: 10.1080/10407790.2014.992094.
   Web of Science ®Google Scholar
• A. Miettinen and T. Siikonen, “Application of pressure-and density-based methods for different flow speeds,” Int. J. Numer. Meth. Fluids, vol. 79, no. 5, pp. 243–267, 2015. DOI: 10.1002/fld.4051.
   Web of Science ®Google Scholar
• F. H. Harlow and A. A. Amsden, “A numerical fluid dynamics calculation method for all flow speeds,” J. Comput. Phys., vol. 8, no. 2, pp. 197–213, 1971. DOI: 10.1016/0021-9991(71)90002-7.
   Web of Science ®Google Scholar
• J. P. Van Doormaal, G. D. Raithby, and B. H. McDonald, “The segregated approach to predicting viscous compressible fluid flows,” In ASME 1986 International Gas Turbine Conference and Exhibit, V001T01A084. American Society of Mechanical Engineers, 1986. DOI: 10.1115/86-GT-196.
   Google Scholar
• K. H. Chen and R. H. Pletcher, “Primitive variable, strongly implicit calculation procedure for viscous flows at all speeds,” AIAA J., vol. 29, no. 8, pp. 1241–1249, 1991. DOI: 10.2514/3.10728.
   Google Scholar
• S. Acharya, B. R. Baliga, K. Karki, J. Y. Murthy, C. Prakash and S. P. Vanka, “Pressure-based finite-volume methods in computational fluid dynamics,” J. Heat Transf., vol. 129, no. 4, pp. 407–424, 2007. DOI: 10.1115/1.2716419.
   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®. Basel, Switzerland: Springer International Publishing, 2015.
   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. DOI: 10.1006/jcph.2000.6683.
   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. Tr. B-Fund., vol. 37, no. 1, pp. 103–139, 2000. DOI: 10.1080/104077900275576.
   Web of Science ®Google Scholar
• A. Cubero and N. Fueyo, “Preconditioning based on a partially implicit implementation of momentum interpolation for coupled solvers,” Numer. Heat. Tr. B-Fund., vol. 53, no. 6, pp. 510–535, 2008. DOI: 10.1080/10407790802035281.
   Web of Science ®Google Scholar
• M. Darwish, I. Sraj and F. Moukalled, “A coupled incompressible flow solver on structured grids,” Numer. Heat. Tr. B-Fund., vol. 52, no. 4, pp. 353–371, 2007. DOI: 10.1080/10407790701372785.
   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. 228, no. 1, pp. 180–201, 2009. DOI: 10.1016/j.jcp.2008.08.027.
   Web of Science ®Google Scholar
• Z. J. Chen and A. J. Przekwas, “A coupled pressure-based computational method for incompressible/compressible flows,” J. Comput. Phys., vol. 229, no. 24, pp. 9150–9165, 2010. DOI: 10.1016/j.jcp.2010.08.029.
   Web of Science ®Google Scholar
• C. N. Xiao, F. Denner and B. G. van Wachem, “Fully coupled pressure-based finite-volume framework for the simulation of fluid flows at all speeds in complex geometries,” J. Comput. Phys., vol. 346, pp. 91–130, 2017. DOI: 10.1016/j.jcp.2017.06.009.
   Web of Science ®Google Scholar
• R. M. Beam and R. F. Warming, “An implicit factored scheme for the compressible Navier-Stokes equations,” AIAA J., vol. 16, no. 4, pp. 393–402, 1978. DOI: 10.2514/3.60901.
   Google Scholar
• R. W. MacCormack, “A numerical method for solving the equations of compressible viscous flow,” AIAA J., vol. 20, no. 9, pp. 1275–1281, 1982. DOI: 10.2514/3.51188.
   Google Scholar
• E. Turkel, R. Radespiel and N. Kroll, “Assessment of preconditioning methods for multidimensional aerodynamics,” Computers Fluids, vol. 26, no. 6, pp. 613–634, 1997. DOI: 10.1016/S0045-7930(97)00013-3.
   Web of Science ®Google Scholar
• T. H. Pulliam, Characteristic boundary conditions for the Euler equations. 1981.
   Google Scholar
• J. R. Carlson, Inflow/outflow boundary conditions with application to FUN3D. 2011.
   Google Scholar
• A. Jameson and D. Mavriplis, “Finite volume solution of the two-dimensional Euler equations on a regular triangular mesh,” AIAA J., vol. 24, no. 4, pp. 611–618, 1986. DOI: 10.2514/3.9315.
   Google Scholar
• S. Mathur and J. Murthy, “All speed flows on unstructured meshes using a pressure correction approach,” In 14th Computational Fluid Dynamics Conference, 1999. p. 3365. DOI: 10.2514/6.1999-3365.
   Google Scholar
• F. Moukalled, L. Mangani and M. Darwish, “The characteristic boundary condition in pressure-based methods,” Numer. Heat. Tr. B-Fund., vol. 76, no. 2, pp. 43–59, 2019. DOI: 10.1080/10407790.2019.1644942.
   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. DOI: 10.1016/j.amc.2010.07.052.
   Web of Science ®Google Scholar
• M. Darwish and F. Moukalled, “A fully coupled Navier-Stokes solver for fluid flow at all speeds,” Numer. Heat. Tr. B-Fund., vol. 65, no. 5, pp. 410–444, 2014. DOI: 10.1080/10407790.2013.869102.
   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. Tr. B-Fund., vol. 67, no. 1, pp. 47–74, 2015. DOI: 10.1080/10407790.2014.949500.
   Web of Science ®Google Scholar
• F. Moukalled, L. Mangani and M. Darwish, “Implementation of boundary conditions in the finite volume pressure-based method-part I: segregated solvers,” Num. Heat Transf. Part B, vol. 69, no. 6, pp. 534–562, 2016. DOI: 10.1080/10407790.2016.1138748.
   Web of Science ®Google Scholar
• L. Mangani, M. Darwish and F. Moukalled, “An openFOAM pressure-based coupled CFD solver for turbulent and compressible flows in turbomachinary applications,” Num. Heat Transf. Part B, vol. 69, no. 5, pp. 413–431, 2016. DOI: 10.1080/10407790.2015.1125212.
   Web of Science ®Google Scholar
• M. Darwish, W. Geahchan and F. Moukalled, “A fully implicit method for coupling multi-block meshes with non-matching interface grids,” Numer. Heat. Tr. B-Fund., vol. 71, no. 2, pp. 109–132, 2017. DOI: 10.1080/10407790.2016.1265299.
   Web of Science ®Google Scholar
• L. Mangani, M. Buchmayr, M. Darwish and F. Moukalled, “A fully coupled openFOAM solver for transient incompressible turbulent flows in ALE formulation,” Numer. Heat. Tr. B-Fund., vol. 71, no. 4, pp. 313–326, 2017. DOI: 10.1080/10407790.2017.1293969.
   Web of Science ®Google Scholar
• F. R. Menter, “Two-equation eddy-viscosity turbulence models for engineering applications,” AIAA J., vol. 32, no. 8, pp. 1598–1605, 1994. DOI: 10.2514/3.12149.
   Web of Science ®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, no. 11, pp. 1525–1532, 1983. DOI: 10.2514/3.8284.
   Google Scholar
• NASA Langley Turbulence Modeling Resource website. http://turbmodels.larc.nasa.gov.
   Google Scholar
• I. Demirdžić, Ž. Lilek and M. Perić, “A collocated finite volume method for predicting flows at all speeds,” Int. J. Numer. Meth. Fluids, vol. 16, no. 12, pp. 1029–1050, 1993. DOI: 10.1002/fld.1650161202.
   Web of Science ®Google Scholar
• A. Nouri-Borujerdi and A. S. Ghazani, “A pressure-based algorithm for internal compressible turbulent flows through a geometrical singularity,” Numer. Heat. Tr. B-Fund., vol. 75, no. 2, pp. 127–117, 2019. DOI: 10.1080/10407790.2019.1612665.
   Web of Science ®Google Scholar
• I. Sezai, “Implementation of boundary conditions in pressure-based finite volume methods on unstructured grids,” Numer. Heat. Tr. B-Fund., vol. 72, no. 1, pp. 82–107, 2017. DOI: 10.1080/10407790.2017.1338077.
   Web of Science ®Google Scholar
• H. Tan, “Applying the free-slip boundary condition with an adaptive cartesian cut-cell method for complex geometries,” Numer. Heat. Tr. B-Fund., vol. 74, no. 4, pp. 661–684, 2018. DOI: 10.1080/10407790.2018.1562770.
   Web of Science ®Google Scholar
• K. R. Laflin, et al., “Data summary from second aiaa computational fluid dynamics drag prediction workshop,” J. Aircraft, vol. 42, no. 5, pp. 1165–1178, 2005. DOI: 10.2514/1.10771.
   Web of Science ®Google Scholar
• T. Barth and D. Jespersen, “The design and application of upwind schemes on unstructured meshes,” In 27th Aerospace Sciences Meeting, 1989. p. 366. DOI: 10.2514/6.1989-366.
   Google Scholar