The characteristic boundary condition in pressure-based methods

References

• A. Jameson, “Solution of the Euler Equations For Two Dimensional Transonic Flow by a Multigrid Method,” Appl. Math. Comput., vol. 13, no. 3-4, pp. 327–356, 1983. DOI: 10.1016/0096-3003(83)90019-X.
   Web of Science ®Google Scholar
• A. Jameson, W. Schmidt, and E. Turkel, “Numerical Solution of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time Stepping Schemes,” AIAA 14th Fluids and Plasma Dynamic Conference, Paper 81-1259, Palo Alto, California, June 23–25, 1981.
   Google Scholar
• A. Jameson, and T. J. Baker, “Solution of the Euler Equations for Complex Configurations”. Proc. 6th AIAA Computational Fluid Dynamics Conference,” AIAA Paper, pp. 293–302, 1983. 83-1929, Danvers, July
   Google Scholar
• M. J. Berger, and A. Jameson, “Automatic Adaptive Grid Refinement for the Euler Equations”. AIAA J., vol. 23, no. 4, pp. 561–568, 1985. DOI: 10.2514/3.8951.
   Google Scholar
• A. Jameson, and S. Wolfgang, “Some Recent Developments in Numerical Methods for Transonic Flows,” Computer Methods Appl. Mech. Eng., vol. 51, no. 1-3, pp. 467–493, 1985. DOI: 10.1016/0045-7825(85)90043-X.
   Web of Science ®Google Scholar
• A. Rizzi, and L. E. Eriksson, “Computation of inviscid incompressible flow with rotation,” J. Fluid Mech., vol. 153, no. 1, pp. 275–312, 1985. DOI: 10.1017/S0022112085001264.
   Google Scholar
• D. Choi, and C. L. Merkle, “Application of time-iterative schemes to incompressible flow,” AIAA J., vol. 23, no. 10, pp. 1518–1524, 1985. DOI: 10.2514/3.9119.
   Google Scholar
• Y. H. Choi, and C. L. Merkle, “The application of preconditioning to viscous flows,” Comput. Phys., vol. 105, no. 2, pp. 207–223, 1993. DOI: 10.1006/jcph.1993.1069.
   Google Scholar
• D. L. Tweedt, R. V. Chima, and E. Turkel, Preconditioning for Numerical Simulation of Low Mach Number Three-Dimensional Viscous Turbomachinary Flows, Technical Paper 97-1828. AIAA Press, Washington, DC, 1997.
   Google Scholar
• J. M. Weiss, and W. A. Simith, “Preconditioning applied to variable and constant density flows,” AIAA J., vol. 33, no. 11, pp. 2050–2057, 1995. DOI: 10.2514/3.12946.
   Google Scholar
• C. L. Merkle, J. Y. Sullivan, P. E. O. Buelow, and S. Venkateswaran, “Computation of flows with arbitrary equations of state,” AIAA J., vol. 36, no. 4, pp. 515–521, 1998. DOI: 10.2514/2.424.
   Google Scholar
• J. R. Edwards, and M. S. Liou, “Low-diffusion flux-splitting methods for flows at all speeds,” AIAA J., vol. 36, no. 9, pp. 1610–1617, 1998. DOI: 10.2514/2.587.
   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 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 Transfer, vol. 7, pp, pp. 147–163, 1984. DOI: 10.1080/01495728408961817.
   Google Scholar
• S. Acharya, and F. Moukalled, “Improvements to incompressible flow calculation on a non-staggered curvilinear grid,” Numer. Heat Transfer, Part B Fundam., vol. 15, pp, pp. 131–152, 1989. DOI: 10.1080/10407798908944897.
   Web of Science ®Google Scholar
• S. V. Patankar, Numerical Heat Transfer and Fluid Flow. New York, 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 Transfer, Part B Fundam., vol. 67, no. 6, pp. 563–589, 2015. DOI: 10.1080/10407790.2014.992094.
   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. DOI: 10.1080/10407790.2014.949500.
   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®. Cham: Springer International Publishing, 2015.
   Google Scholar
• K. C. Karki, A calculation procedure for viscous flows at all speeds in complex geometries, Ph.D. thesis (University of Minnesota, 1986).
   Google Scholar
• C. H. Marchi, and C. R. Maliska, “A non-orthogonal finite-volume methods for the solution of all speed flows using co-located variables,” Numer. Heat Transfer, Part B Fundam., vol. 26, no. 3, pp. 293–311, 1994. DOI: 10.1080/10407799408914931.
   Web of Science ®Google Scholar
• I. Demirdzic, Z. Lilek, and M. Peric, “A Collocated finite volume method for predicting flows at all speeds,” Int. J. Numer. Methods Fluids, vol. 16, pp. 1029–1050, 1993. DOI: 10.1002/fld.1650161202.
   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. DOI: 10.1080/104077900275576.
   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 Transfer, Part B Fundam., vol. 72, no. 1, pp. 82–107, 2017. DOI: 10.1080/10407790.2019.1612665.
   Google Scholar
• I. Sezai, “Implementation of boundary conditions in pressure-based finite volume methods on unstructured grids,” Numer. Heat Transfer, Part B Fundam., vol. 75, no. 2, pp. 127–143, 2019. DOI: 10.1080/10407790.2017.1338077.
   Google Scholar
• H. Tan, “Applying the free-slip boundary condition with an adaptive cartesian cut-cell method for complex geometries,” Numer. Heat Transfer, Part B Fundam., vol. 74, no. 4, pp. 661–684, 2018. DOI: 10.1080/10407790.2018.1562770.
   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,” Numer. Heat Transfer, Part B Fundam., vol. 69, no. 6, pp. 534–562, 2016. DOI: 10.1080/10407790.2016.1138748.
   Web of Science ®Google Scholar
• Pulliam, T. “Characteristic Boundary Conditions for the Euler Equations,” Proceeding of Symposium on Numerical Boundary Condition Procedures NASA CP–2201, pp. 165–181, 1981.
   Google Scholar
• J. Carlson, “Inflow/Outflow Boundary Conditions with Application to FUN3D,” NASA/TM-2011-217181, 2011.
   Google Scholar
• A. Jameson, and D. Mavriplis, “Finite Volume Solution of the Two-Dimensional Euler Equations on a Regular Triangular Mesh,” AIAA 23rd Aerospace Sciences Meeting, Reno, Nevada, January 14–17, AIAA-85-0435, 1985.
   Google Scholar
• S. R. Mathur, and J. Y. Murthy, “All Speed Flows on Unstructured Meshes Using a Pressure Correction Approach,” AIAA 14th Computational Fluid Dynamics Conference-Norfolk, VA. USA, November 1–5, 1999 (paper # AIAA-99-3365).
   Google Scholar
• P. R. Spalart, and S. R. Allmaras, “A One-Equation Turbulence Model for Aerodynamic Flows,” Recherche Aerospatiale, no. 1, pp. 5–21, 1994.
   Google Scholar
• P. R. Spalart, “Trends in Turbulence Treatments,” Fluids 2000 Conference and Exhibit, paper no. AIAA 2000-2306, June 2000.
   Google Scholar
• P. R. Spalart, and C. L. Rumsey, “Effective inflow conditions for turbulence models in aerodynamic calculations,” AIAA J., vol. 45, no. 10, pp. 2544–2553, 2007. DOI: 10.2514/1.29373.
   Google Scholar
• I. Demirdzic, A Finite Volume Method for Computation of Fluid Flow in Complex Geometries, Ph.D. Thesis, University of London, 1982.
   Google Scholar
• S. Muzaferija, Adaptive Finite Volume Method for Flow Predictions Using Unstructured Meshes and Multigrid Approach, Ph.D. thesis, University of London, 1994.
   Google Scholar
• I. Demirdzic, and S. Musaferija, “Numerical method for coupled fluid flow, heat transfer and stress analysis using unstructured moving meshes with cells of arbitrary topology,” Comput. Methods Appl. Mech. Eng., vol. 125, pp. 235–255, 1995.
   Web of Science ®Google Scholar
• S. R. Mathur, and J. Y. Murthy, “A pressure-based method for unstructured meshes,” Numer. Heat Transfer, Part B Fundam., vol. 31, no. 2, pp. 195–215, 1997. DOI: 10.1080/10407799708915105.
   Web of Science ®Google Scholar
• H. Jasak, Error Analysis and Estimation for the Finite Volume Method with Applications to Fluid Flow, PhD. thesis, Imperial College, London, 1996.
   Google Scholar
• I. Demirdzic, “On the discretization of the diffusion term in finite-volume continuum mechanics,” Numer. Heat Transfer, Part B Fundam., vol. 68, no. 1, pp. 1–10, 2015.
   Web of Science ®Google Scholar
• B. P. Leonard, “Locally modified quick scheme for highly convective 2-D and 3-D flows,” in Numerical Methods in Laminar and Turbulent Flows, vol. 5, C. Taylor and K. Morgan, (Eds.). Swansea, U.K.: Pineridge Press, 1987, pp. 35–47.
   Google Scholar
• S. G. Rubin, and P. K. Khosla, “Polynomial interpolation method for viscous flow calculations,” J. Comput. Phys., vol. 27, pp. 153–168, 1982.
   Google Scholar
• F. Moukalled, and M. Darwish, “Transient schemes for capturing interfaces of free-surface flows,” Numer. Heat Transfer, Part B Fundam., vol. 61, no. 3, pp. 171–203, 2012. DOI: 10.1080/10407790.2012.666145.
   Web of Science ®Google Scholar
• C. M. Rhie, and W. L. Chow, “A numerical study of the turbulent flow past an isolated airfoil with trailing edge separation,” AIAA J., vol. 21, no. 11, pp. 1525–1532, 1983. DOI: 10.2514/3.8284.
   Google Scholar
• Turbulence Modeling Resource. Available: https://turbmodels.larc.nasa.gov/index.html
   Google Scholar
• K. Wieghardt, and W. Tillman, “On the turbulent friction layer for rising pressure,” NACA TM-1314, 1951.
   Google Scholar
• W. D. Bachalo, and D. A. Johnson, “Transonic, turbulent boundary-layer separation generated on an axisymmetric flow model,” AIAA J., vol. 24, no. 3, pp. 437–443, 1986. DOI: 10.2514/3.9286.
   Google Scholar
• N. Gregory, and C. L. O'reilly, ” Low-Speed Aerodynamic Characteristics of NACA 0012 Aerofoil Section, including the Effects of Upper-Surface Roughness Simulating Hoar Frost,” Aeronautical Research Council, Aerodynamics Division N.P.L., Reports and Memoranda No. 3726, London, January, 1970.
   Google Scholar
• V. Schmitt, and F. Charpin, “Pressure Distributions on the ONERA-M6-Wing at Transonic Mach Numbers,” Experimental Data Base for Computer Program Assessment. Report of the Fluid Dynamics Panel Working Group 04, AGARD AR 138, May 1979.
   Google Scholar