An Artificial Viscosity for the III-Posed One-Dimensional Incompressible Two-Fluid Model

REFERENCES

• J. D. Ramshaw and J. A. Trapp, “Characteristics, Stability and Short-Wavelength Phenomena in Two-Phase Flow Equation Systems”, Nucl. Sci. Eng., 66, 93 (1978).
   Web of Science ®Google Scholar
• W. D. Fullmer, V. H. Ransom, and M. A. Lopez de Bertodano, “Linear and Nonlinear Analysis of an Unstable, but Well-Posed, One-Dimensional Two-Fluid Model for Two-Phase Flow Based on the Inviscid Kelvin-Helmholtz Instability”, Nucl. Eng. Des., 268, 173 (2014); http://dx.doi.org/10.1016/j.nucengdes.2013.04.043.
   Google Scholar
• W. D. Fullmer, V. H. Ransom, and M. A. Lopez de Bertodano, “Assessment of Regularization Methods for the 1D Two-Fluid Model”, Trans. Am. Nucl. Soc., 106, 988 (2012).
   Google Scholar
• M.-S. Liou et al., “Hyperbolicity, Discontinuities, and Numerics of Two-Fluid Models,” Computational Fluid Dynamics, p. 625, H. Deconinck and E. Dick, Eds., Springer-Verlag, Berlin (2006).
   Google Scholar
• J.-M. Ghidaglia, A. Kumbaro, and G. Le Coq, “On the Numerical Solution of Two-Fluid Models via a Cell Centered Finite Volume Method”, Eur. J. Mech. B. Fluids, 20, 841 (2001); http://dx.doi.org/10.1016/S0997-7546(01)01150-5.
   Google Scholar
• H. Pokharna, M. Mori, and V. H. Ransom, “Regularization of Two-Phase Flow Models: A Comparison of Numerical and Differential Approaches”, J. Comput.. Phys., 134, 282 (1997); http://dx.doi.org/10.1006/jcph.1997.5695.
   Google Scholar
• R. Krishnamurthy and V. H. Ransom, “A NonLinear Stability Study of the RELAP5/MOD3 Two-Phase Model,” presented at Japan-U.S. Seminar Two-Phase Flow Dynamics, Berkeley, California, July 5-11, 1992.
   Google Scholar
• “RELAP5/MOD3.3 Code Manual, Vol. 5: Users Guidelines,” p3 ed., Information Systems Laboratories (2006).
   Google Scholar
• “TRACE V5.0 User’s Manual Vol. 2: Modeling Guidelines,” U.S. Nuclear Regulatory Commission (2007).
   Google Scholar
• P. Daripa and W. Hua, “A Numerical Study of an Ill-Posed Boussinesq Equation Arising in Water Waves and Nonlinear Lattices: Filtering and Regularization Techniques”, Appl. Math. Comput, 101, 159 (1999); http://dx.doi.org/10.1016/S0096-3003(98)10070-X.
   Google Scholar
• A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems, V. H. Winston, Washington D.C. (1977).
   Google Scholar
• H. Holmas et al., “Analysis of a 1D Incompressible Two-Fluid Model Including Artificial Diffusion,” IMA J. Appl. Math., 73, 651 (2008); http://dx.doi.org/10.1093/imamat/hxm066.
   Google Scholar
• H. Holmas, “Numerical Simulation of Transient Roll-Waves in Two-Phase Pipe Flow”, Chem. Eng. Sci., 65, 1811 (2010); http://dx.doi.org/10.1016/j.ces.2009.11.031.
   Google Scholar
• M. Ishii and T. Hibiki, Thermo-Fluid Dynamics of Two-Phase Flow, 1st ed., Springer, New York (2006).
   Google Scholar
• “TRACE V5.0 Theory Manual: Field Equations, Solution Methods and Physical Models,” U.S. Nuclear Regulatory Commission (2007).
   Google Scholar
• “RELAP5/MOD3.3 Code Manual, Vol. 1: Code Structure, System Models, and Solution Methods,” p3 ed., Information Systems Laboratories (2003).
   Google Scholar
• W. D. Fullmer, M.A. Lopez de Bertodano, and X. Zhang, “Verification of a Higher-Order Finite Difference Scheme for the One-Dimensional Two-Fluid Model,” J. Comput. Multiphase Flows, 5, 139 (2013); http://dx.doi.org/10.1260/1757-482X.5.2.139.
   Google Scholar
• J. C. Tannehill, D. A. Anderson, and R. H. Pletcher, Computational Fluid Mechanics and Heat Transfer, 2nd ed., Taylor & Francis, Philadelphia, Pennsylvania (1997).
   Google Scholar
• “Mathematica,” Version 8.0, Wolfram Research (2010).
   Google Scholar
• R. D. Richtmyer and K. W. Morton, Difference Methods for Initial-Value Problems, 2nd ed., Interscience, New York (1967).
   Google Scholar
• D. Gidaspow, “Round Table Discussion (RT-1-2): Modeling of Two-Phase Flow,” Proc. 5th Int. Heat Transfer Conf., Tokyo, Japan, September 3-7, 1974.
   Google Scholar
• V. H. Ransom, “Benchmark Numerical Tests,” Multiphase Science and Technology, 3rd ed., G. F. Hewitt, J. M. Delhay, and N. Zuber, Eds., Hemisphere, Washington D.C., (1987).
   Google Scholar
• V. H. Ransom and V. Mousseau, “Convergence and Accuracy of the RELAP5 Two-Phase Flow Model,” Proc. Int. Topl. Mtg. Advances in Mathematics, Computations and Reactor Physics, Pittsburgh, Pennsylvania, April 28-May 2, 1991, American Nuclear Society (1991).
   Google Scholar
• J. H. Stuhmiller, “The Influence of Interfacial Pressure Forces on the Character of Two-Phase Flow Model Equations”, Int. J. Multiphase Flow, 3, 551 (1977); http://dx.doi.org/10.1016/0301-9322(77)90029-5.
   Google Scholar