An appropriate numerical dissipation for SLAU2 towards shock-stable compressible multiphase flow simulations

[1] H. Tamura, M. Takahashi, M. Sasaki, T. Tomita, W. Mayer, Observation of LOX/hydrogen combustion flame in a rocket chamber during chugging instability, in: 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 2003.

[2] R.W. Houim, E.S. Oran, A multiphase model for compressible granular–gaseous flows: formulation and initial tests, J. Fluid Mech. 789 (2016) 166–220.

[3] M.-S. Liou, C.-H. Chang, L. Nguyen, T.G. Theofanous, How to solve compressible multifluid equations: a simple, robust, and accurate method, AIAA J.

46 (9) (2008) 2345–2356.

[4] J. Stuhmiller, The influence of interfacial pressure forces on the character of two-phase flow model equations, Int. J. Multiph. Flow 3 (6) (1977) 551–560.

[5] S.K. Godunov, Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics, Mat. Sb. 47(89) (3)

(1959) 271–306.

[6] K. Kitamura, M.-S. Liou, C.-H. Chang, Extension and comparative study of AUSM-family schemes for compressible multiphase flow simulations, Commun. Comput. Phys. 16 (3) (2014) 632–674.

[7] J.J. Quirk, A contribution to the great Riemann solver debate, Int. J. Numer. Methods Fluids 18 (6) (1994) 555–574.

[8] M.-S. Liou, Mass flux schemes and connection to shock instability, J. Comput. Phys. 160 (2) (2000) 623–648.

[9] Y.-Y. Niu, Y.-C. Lin, C.-H. Chang, A further work on multi-phase two-fluid approach for compressible multi-phase flows, Int. J. Numer. Methods Fluids

58 (8) (2008) 879–896.

10

J. Aono and K. Kitamura

Journal of Computational Physics 462 (2022) 111256

[10] A.K. Pandare, H. Luo, A robust and efficient finite volume method for compressible inviscid and viscous two-phase flows, J. Comput. Phys. 371 (2018)

67–91.

[11] M.-S. Liou, A sequel to AUSM, part II: AUSM+-up for all speeds, J. Comput. Phys. 214 (1) (2006) 137–170.

[12] E. Shima, K. Kitamura, Parameter-free simple low-dissipation AUSM- family scheme for all speeds, AIAA J. 49 (8) (2011) 1693–1709.

[13] E. Shima, K. Kitamura, Multidimensional numerical noise from captured shock wave and its cure, AIAA J. 51 (4) (2013) 992–998.

[14] K. Kitamura, E. Shima, Towards shock-stable and accurate hypersonic heating computations: a new pressure flux for AUSM-family schemes, J. Comput.

Phys. 245 (2013) 62–83.

[15] K. Kitamura, A. Hashimoto, Reduced dissipation AUSM-family fluxes: HR-SLAU2 and HR-AUSM+-up for high resolution unsteady flow simulations,

Comput. Fluids 126 (2016) 41–57.

[16] K. Kitamura, S. Nonaka, K. Kuzuu, J. Aono, K. Fujimoto, E. Shima, Numerical and experimental investigations of epsilon launch vehicle aerodynamics at

Mach 1.5, J. Spacecr. Rockets 50 (4) (2013) 896–916.

[17] T. Aogaki, K. Kitamura, S. Nonaka, Numerical study on high angle-of-attack pitching moment characteristics of slender-bodied reusable rocket, J. Spacecr.

Rockets 55 (6) (2018) 1476–1489.

[18] M.E. Harvazinski, T. Shimizu, Computational investigation on the effect of the oxidizer inlet temperature on combustion instability, in: AIAA Propulsion

and Energy 2019 Forum, 2019.

[19] C.-H. Chang, M.-S. Liou, A robust and accurate approach to computing compressible multiphase flow: stratified flow model and AUSM+-up scheme,

J. Comput. Phys. 225 (1) (2007) 840–873.

[20] V. Ransom, Numerical benchmark tests, in: G.F. Hewitt, J.M. Delhay, N. Zuber (Eds.), Multiphase Science and Technology, vol. 3, 1987, pp. 465–467.

[21] F. Harlow, A. Amsden, Fluid Dynamics, Technical Report LA-4700, 1971.

[22] H.B. Stewart, B. Wendroff, Two-phase flow: models and methods, J. Comput. Phys. 56 (3) (1984) 363–409.

[23] B. van Leer, Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method, J. Comput. Phys. 32 (1) (1979)

101–136.

[24] G.D. van Albada, B. van Leer, W.W. Roberts, A Comparative Study of Computational Methods in Cosmic Gas Dynamics, Springer Berlin Heidelberg,

Berlin, Heidelberg, 1997, pp. 95–103.

[25] S. Gottlieb, C.-W. Shu, Total variation diminishing Runge-Kutta schemes, Math. Comput. 67 (221) (1998) 73–85.

[26] J. Edwards, Towards unified CFD simulations of real fluid flows, in: 15th AIAA Computational Fluid Dynamics Conference, 2001.

[27] H. Paillére, C. Corre, J.G. Cascales, On the extension of the AUSM+ scheme to compressible two-fluid models, Comput. Fluids 32 (6) (2003) 891–916.

[28] H. Takahira, S. Yuasa, Numerical Simulations of Shock-Bubble Interactions Using an Improved Ghost Fluid Method Volume 1: Symposia, Parts A and B,

2005, pp. 777–785.

[29] A.K. Pandare, H. Luo, J. Bakosi, An enhanced AUSM+ -up scheme for high-speed compressible two-phase flows on hybrid grids, Shock Waves 29 (2019)

629–649.

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