Study of high-order-accurate limiters for time-dependent contact discontinuity and shock capturing

References

• R. Abgrall, How to Prevent Pressure Oscillations in Multicomponent Flow Calculations: Quasi Conservative Approach, J. of Comput. Phys., vol. 125, pp. 150–160, 1996.
   Web of Science ®Google Scholar
• T. Buffard, T. Gallouet, and J. M. Hérard, A Sequel to a Rough Godunov Scheme: Application to Real Gases, Comput. Fluids, vol. 29, pp. 813–847, 2000.
   Web of Science ®Google Scholar
• M. Čada, Compact Third-Order Limiter Functions for Finite Volume Methods, Dipl. Geo Physiker, Ludwig-Maximilians University, 2009.
   Google Scholar
• Y. A. Çengel, and A. B. Michael, Fundamentals of Thermodynamics, McGraw-Hill, New York, 2002.
   Google Scholar
• R. M. L. Coelho, P. L. C. Lage, and A. S. Telles, A Comparison Of Hyperbolic Solvers for Ideal and Real Gas Flows, Brazil. J. Chem. Eng., vol. 23, pp. 301–318, 2006.
   Web of Science ®Google Scholar
• S. K. Godunov, A Difference Method for Numerical Calculation of Discontinuous Equation of Hydrodynamics, Math Sbornik, vol. 47, pp. 217–306, 1959 (in Russian).
   Google Scholar
• A. Jameson, W. Schmidt, and E. Turkel, Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes, AIAA Paper 1981–1259, 1981.
   Google Scholar
• P. Jenny, B. Mueller, and H. Thomann, Correction of Conservative Euler Solvers for Gas Mixtures, J. Comput. Phys., vol. 132, pp. 91–107, 1997.
   Web of Science ®Google Scholar
• J. R. Kamm and M. Shashkov, A Pressure Relaxation Closure Model for One-Dimensional, Two-Material Lagrangian Hydrodynamics Based on the Riemann Problem, Tech. Rep. LA-UR-09-00659, Los Alamos National Laboratory, 2009.
   Google Scholar
• S. Karni, Multicomponent Flow Calculations by a Consistent Primitive Algorithm, J. Comput. Phys., vol. 112, pp. 31–43, 1994.
   Web of Science ®Google Scholar
• F. Kemm, A Comparative Study of TVD-Limiters—Well-Known Limiters and an Introduction of New Ones, Int. J. Numer. Meth. Fluids, vol. 67, pp. 404–440, 2011.
   Web of Science ®Google Scholar
• K. H. Kim, C. Kim, and O. H. Rho, Methods for the Accurate Computations of Hypersonic Flows: I. AUSMPW+ Schemes, J. Comput. Phys., vol. 174, pp. 38–80, 2001.
   Web of Science ®Google Scholar
• M. S. Liou and C. J. Steffen, A Flux Splitting Scheme, NASA TM104404, 1991; J. Comput. Phys., vol. 107, pp. 23–39, 1991.
   Web of Science ®Google Scholar
• J. M. Masella, I. Faille, and T. Gallouet, On An Approximate Godunov Scheme, J. Comput. Fluid Dynam., vol. 12, pp. 133–149, 1999.
   Web of Science ®Google Scholar
• R. Menikoff and B. J. Plhor, The Riemann Problem for Fluid Flow of Real Materials, Rev. Mod. Phys., vol. 61, pp. 75–131, 1989.
   Web of Science ®Google Scholar
• K. H. Prendergast and K. Xu Numerical Hydrodynamics from Gas-Kinetic Theory, J. Comput. Phys., vol. 109, pp. 53–66, 1993.
   Web of Science ®Google Scholar
• L. B. Richard and J. F. Douglas, Numerical Analysis, 8th ed. Thomson Brooks/Cole, Belmont, CA, 2005.
   Google Scholar
• T. H. Shieh, Technical Report and Thesis, Section of Aerothermodynamics of Institute for Fluidmechanics of German Aerospace Center (DLR) and Institute for Turbomachinery and Fluiddynamics of University Hannover, 1999.
   Google Scholar
• T. H. Shieh and M. R. Li, Numeric Treatment of Contact Discontinuity with Multi Gases, J. Comput. Appl. Math., vol. 230, pp. 656–673, 2009.
   Web of Science ®Google Scholar
• P. K. Sweby, High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws, J. Numer. Anal., vol. 21, pp. 995–1011, 1984.
   Web of Science ®Google Scholar
• E. F. Toro and S. J. Billett, Centred TVD Schemes for Hyperbolic Conservation Laws, J. Numer. Anal., vol. 20, pp. 47–79, 2000.
   Web of Science ®Google Scholar
• B. van Leer, Upwind and High-Resolution Methods for Compressible Flow: From Donor Cell to Residual-Distribution Schemes, Commun. Comput. Phys., vol. 1, pp. 192–206, 2006.
   Web of Science ®Google Scholar
• Y. Wada and M. S. Liou A Flux Splitting Scheme with High-Resolution and Robustness for Discontinuities, AIAA-94-0083, 1994.
   Google Scholar
• K. Xu and K. H. Prendergast, Numerical Navier-Stokes Solutions from Gas Kinetic Theory, J. Comput. Phys., vol. 114, pp. 9–17, 1994.
   Web of Science ®Google Scholar
• M. Zijlema and P. Wesseling, Higher-Order Flux-Limiting Schemes for the Finite Volume Computation of Incompressible Flow, Int. J. Comput. Fluid Dynam., vol. 9, issue 2, pp. 89–109, 1998.
   Web of Science ®Google Scholar