A hybrid flux splitting method for compressible flow

References

• J. L. Steger and R. F. Warming, “Flux vector splitting of the inviscid gas-dynamic equations with application to finite-difference methods,” J. Comput. Phys., vol. 40, pp. 263–293, 1981. DOI: 10.1016/0021-9991(81)90210-2.
   Web of Science ®Google Scholar
• B. van Leer, “Flux-vector splitting for the Euler equations,”Proceedings of 8th International Conference on Numerical Methods in Fluid Dynamics, Berlin, vol. 170, Springer, pp. 507–512, 1982.
   Google Scholar
• P. L. Roe, “Approximate Riemann solvers, parameter vectors, and difference schemes,” J. Comput. Phys., vol. 43, pp. 357–372, 1981. DOI: 10.1006/jcph.1997.5705.
   Web of Science ®Google Scholar
• B. Einfeldt, “On Godunov-type methods for gas dynamics,” SIAM J. Numer. Anal., vol. 25, pp. 294–318, 1988. DOI: 10.1137/0725021.
   Web of Science ®Google Scholar
• M. S. Liou and C. J. Steffen, “A new flux splitting scheme,” J. Comput. Phys., vol. 107, pp. 23–39, 1993. DOI: 10.1006/jcph.1993.1122.
   Web of Science ®Google Scholar
• F. Qu, C. Yan, J. Yu, and D. Sun, “A new flux splitting scheme for the Euler equations,” Comput. Fluids, vol. 102, pp. 203–214, 2014. DOI: 10.1016/j.compfluid.2014.07.004.
   Web of Science ®Google Scholar
• M. S. Liou, “A sequel to AUSM: AUSM+,” J. Comput. Phys., vol. 129, pp. 364–382, 1996. DOI: 10.1006/jcph.1996.0256.
   Web of Science ®Google Scholar
• Y. Wada and M. S. Liou, “A flux splitting scheme with high-resolution and robustness for discontinuities,”AIAA Paper 94–0083. Washington, DC: AIAA Press, 1994.
   Google Scholar
• K. H. Kim, C. Kim, and O.-H. Rho, “Methods for the accurate computations of hypersonic flows I. AUSMPW+ scheme,” J. Comput. Phys., vol. 174, pp. 38–80, 2001. DOI: 10.1006/jcph.2001.6873.
   Web of Science ®Google Scholar
• M. S. Liou, “A sequel to AUSM, part II: AUSM+-up for all speeds,” J. Comput. Phys., vol. 214, pp. 137–170, 2006. DOI: 10.1016/j.jcp.2005.09.020.
   Web of Science ®Google Scholar
• K. Peery and S. Imlay, “Blunt-body flow simulations,” AIAA Paper 88–2904. Washington, DC: AIAA Press, 1988.
   Google Scholar
• J. J. Quirk, “A contribution to the great Riemann solver debate,” Int. J. Numer. Methods Fluids, vol. 18, pp. 555–574, 1994. DOI: 10.1007/978-3-642-60543-7_22.
   Web of Science ®Google Scholar
• M. Pandolfi and D. D’Ambrosio, “Numerical instabilities in upwind methods: Analysis and cures for the “Carbuncle” phenomenon,” J. Comput. Phys., vol. 166, pp. 271–301, 2001. DOI: 10.1006/jcph.2000.6652.
   Web of Science ®Google Scholar
• M. S. Liou, “Mass flux schemes and connection to shock instability,” J. Comput. Phys., vol. 160, pp. 623–648, 2000. DOI: 10.1006/jcph.2000.6478.
   Web of Science ®Google Scholar
• J. Gressier and J. M. Moschetta, “Robustness versus accuracy in shock-wave computations,” Int. J. Numer. Methods Fluids, vol. 33, pp. 313–332, 2000. DOI: 10.1002/1097-0363(20000615)33:3<313::aid-fld7>3.3.co;2-5.
   Web of Science ®Google Scholar
• M. V. Ramalho, J. H. A. Azevedo, and J. L. F. Azevedo, “Further investigation into the origin of the carbuncle phenomenon in aerodynamic simulations,” Proceedings of 49th AIAA Aerospace Sciences Meeting, Orlando, Florida, 2011.
   Google Scholar
• K. Xu, “Gas evolution dynamics in Godunov-type schemes and analysis of numerical shock instability.” NASA Langley Research Center, Hampton, VA, Rept. 99–6, 1999.
   Google Scholar
• V. Elling, “The carbuncle phenomenon is incurable,” ACTA Math. Sci., vol. 29, pp. 1647–1656, 2009. DOI: 10.1016/s0252-9602(10)60007-0.
   Web of Science ®Google Scholar
• R. W. MacCormack, “Carbuncle computational fluid dynamics problem for blunt-body flows,” J. Aerosp. Inform. Syst., vol. 10, pp. 229–239, 2013. DOI: 10.2514/1.53684.
   Web of Science ®Google Scholar
• W. Xie, H. Li, Z. Tian, and S. Pan, “A low diffusion flux splitting method for inviscid compressible flows,” Comput. Fluids, vol. 112, pp. 83–93, 2015. DOI: 10.1016/j.compfluid.2015.02.004.
   Web of Science ®Google Scholar
• M. S. Liou, B. V. Leer, and J. S. Shuen, “Splitting of inviscid fluxes for real gases,” J. Comput. Phys., vol. 87, pp. 1–24, 1990. DOI: 10.1016/0021-9991(89)90195-2.
   Web of Science ®Google Scholar
• B. van Leer, “Flux-vector splitting for the 1990s,” Cleveland, OH: NASA, Rept. CP- 3078, 1991.
   Google Scholar
• A. Kurganov and E. Tadmor, “Solution of two-dimensional riemann problems for gas dynamics without Riemann problem solvers,” Numer. Method Part. Diff. Eq., vol. 18, pp. 584–608, 2002. DOI: 10.1002/num.10025.
   Web of Science ®Google Scholar
• N. Kwatra, J. Su, J. T. Gretarsson, and R. Fedkiw, “A method for avoiding the acoustic time step restriction in compressible flow,” J. Comput. Phys., vol. 228, pp. 4146–4161, 2009. DOI: 10.1016/j.jcp.2009.02.027.
   Web of Science ®Google Scholar
• J. C. Mandal and V. Panwar, “Robust HLL-type Riemann solver capable of resolving contact discontinuity,” Comput. Fluids, vol. 63, pp. 148–164, 2012. DOI: 10.1016/j.compfluid.2012.04.005.
   Web of Science ®Google Scholar
• J. H. Lee and O. H. Rho, “Accuracy of AUSM+ scheme in hypersonic blunt body flow calculation,” AIAA Paper 98–1538. Washington, DC: AIAA Press, 1988.
   Google Scholar
• M. S. Holden, J. M. Kolly, and S. C. Martin, “Shock/shock interaction heating in laminar and low-density hypersonic flows,”AIAA Paper 96–1866. Washington, DC: AIAA Press, 1996.
   Google Scholar