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Simple and robust HLLC extensions of two-fluid AUSM for multiphase flow computations. (English) Zbl 1391.76480

Summary: A two-fluid AUSM+-up numerical flux function with the exact (Godunov) Riemann solver for the stratified flow model concept by C.-H. Chang et al. [“Hyperbolicity, discontinuities and numerics of the two-fluid model”, in: ASME. Fluids engineering division summer meeting, Volume 1: Symposia, Parts A and B. 635–644 (2007; doi:10.1115/fedsm2007-37338)] has been extended for simple and robust computations of compressible multiphase flows. The present method replaces the Godunov part with the HLLC approximate Riemann solver with no-iteration procedure in a very simple manner: this two-fluid HLLC has been inspired by the work by X. Y. Hu et al. [J. Comput. Phys. 228, No. 17, 6572–6589 (2009; Zbl 1261.76023)], but used in a totally different way. Numerical tests demonstrate that the present two-fluid AUSM+-up is, if only velocity and pressure in the middle zone are computed by HLLC, as robust as the original, Godunov-combined AUSM+-up, despite being free from iterations and convergence criteria.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs

Citations:

Zbl 1261.76023
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[1] Toro, E. F.; Spruce, M.; Speares, W., Restoration of the contact surface in the HLL-Riemann solver, Shock Waves, 4, 25-34, (1994) · Zbl 0811.76053
[2] Toro, E. F., Riemann solvers and numerical methods for fluid dynamics: a practical introduction, (2009), Springer-Verlag Berlin · Zbl 1227.76006
[3] Harten, A.; Lax, P. D.; van Leer, B., On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM Rev, 25, 1, 35-61, (1983) · Zbl 0565.65051
[4] Park, S. H.; Lee, J. E.; Kwon, J. H., Preconditioned HLLE method for flows at all Mach numbers, AIAA J, 44, 11, 2645-2653, (2006)
[5] Abdol-Hamid K, Ghaffari F, Parlette EB. Overview of Ares-I CFD ascent aerodynamic data development and analysis based on USM3D. AIAA paper 2011-15; 2011.
[6] Berger M, Aftosmis MJ. Progress towards a Cartesian cut-cell method for viscous compressible flow. AIAA paper 2012-1301; 2012.
[7] Kidron, Y.; Mor-Yossef, Y.; Levy, Y., Robust Cartesian grid flow solver for high-Reynolds-number turbulent flow simulations, AIAA J, 48, 6, 1130-1140, (2010)
[8] Harris, R.; Wang, Z. J.; Liu, Y., Efficient quadrature-free high-order spectral volume method on unstructured grids: theory and 2D implementation, J Comput Phys, 227, 1620-1642, (2008) · Zbl 1134.65070
[9] Nichols RH, Tramel RW, Buning PG. Solver and turbulence model upgrades to OVERFLOW 2 for unsteady and high-speed applications. AIAA paper 2006-2824; 2006.
[10] Balsara, D. S., Multidimensional HLLE Riemann solver: application to Euler and magnetohydrodynamic flow, J Comput Phys, 229, 1970-1993, (2010) · Zbl 1303.76140
[11] Hanawa, T.; Mikami, H.; Matsumoto, T., Improving shock irregularities based on the characteristics of the MHD equations, J Comput Phys, 227, 7952-7976, (2008) · Zbl 1268.76038
[12] Saurel, R.; Abgrall, R., A multiphase Godunov method for compressible multifluid and multiphase flows, J Comput Phys, 150, 425-467, (1999) · Zbl 0937.76053
[13] Kitamura, K.; Shima, E.; Nakamura, Y.; Roe, P. L., Evaluation of Euler fluxes for hypersonic heating computations, AIAA J, 48, 763-776, (2010)
[14] Shukla, R. K.; Pantano, C.; Freund, J. B., An interface capturing method for the simulation of multi-phase compressible flows, J Comput Phys, 229, 7411-7439, (2010) · Zbl 1425.76289
[15] Saurel, R.; Petitpas, F.; Berry, R. A., Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures, J Comput Phys, 228, 1678-1712, (2009) · Zbl 1409.76105
[16] Nonomura, T.; Morizawa, S.; Terashima, H.; Obayashi, S.; Fujii, K., Numerical (error) issues on compressible multicomponent flows using a high-order differencing scheme: weighted compact nonlinear scheme, J Comput Phys, 231, 3181-3210, (2012) · Zbl 1402.76087
[17] Chang, C.-H.; Liou, M.-S., A robust and accurate approach to computing compressible multiphase flow: stratified flow model and AUSM^{+}-up scheme, J Comput Phys, 225, 840-873, (2007) · Zbl 1192.76030
[18] Liou, M.-S., A sequel to AUSM, part II: AUSM^{+}-up for all speeds, J Comput Phys, 214, 137-170, (2006) · Zbl 1137.76344
[19] Shima, E.; Kitamura, K., Parameter-free simple low-dissipation AUSM-family scheme for all speeds, AIAA J, 49, 8, 1693-1709, (2011)
[20] Kitamura, K.; Shima, E., Towards shock-stable and accurate hypersonic heating computations: a new pressure flux for AUSM-family schemes, J Comput Phys, 245, 62-83, (2013) · Zbl 1349.76487
[21] Kim, S. S.; Kim, C.; Rho, O. H.; Hong, S. K., Methods for the accurate computations of hypersonic flows I. AUSMPW+ scheme, J Comput Phys, 174, 38-80, (2001) · Zbl 1106.76421
[22] Liou, M.-S.; Chang, C.-H.; Nguyen, L.; Theofanous, T. G., How to solve compressible multifluid equations: a simple, robust, and accurate method, AIAA J, 46, 2345-2356, (2008)
[23] Kitamura K, Liou M-S. Comparative study of AUSM-family schemes in compressible multiphase flow simulations. In: ICCFD7-3702, seventh international conference on computational fluid dynamics (ICCFD7). Big Island, Hawaii; July 9-13, 2012 [to be published in Communications in Computational Physics].
[24] Paillère, H.; Corre, C.; Cascales, J. R.G., On the extension of the AUSM+ scheme to compressible two-fluid models, Comput Fluids, 32, 891-916, (2003) · Zbl 1040.76044
[25] Niu, Y.-Y.; Lin, Y.-C.; Chang, C.-H., A further work on multi-phase two-fluid approach for compressible multi-phase flows, Int J Numer Meth Fluids, 58, 879-896, (2008) · Zbl 1213.76126
[26] Stewart, H. B.; Wendroff, B., Two-phase flow: models and methods, J Comput Phys, 56, 363-409, (1984) · Zbl 0596.76103
[27] Godunov, S. K., A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics, Matematicheskii Sbornik/Izdavaemyi Moskovskim Matematicheskim Obshchestvom, 47, 3, 271-306, (1959) · Zbl 0171.46204
[28] Hu, X. Y.; Adams, N. A.; Iaccarino, G., On the HLLC Riemann solver for interface interaction in compressible multi-fluid flow, J Comput Phys, 228, 6572-6589, (2009) · Zbl 1261.76023
[29] Chang, C. H.; Deng, X.; Theofanous, T. G., Direct numerical simulation of interfacial instabilities: a consistent, conservative, all-speed, sharp-interface method, J Comput Phys, 242, 946-990, (2013) · Zbl 1299.76097
[30] Hawker, N. A.; Ventikos, Y., Interaction of a strong shockwave with a gas bubble in a liquid medium: a numerical study, J Fluid Mech, 701, 59-97, (2012) · Zbl 1248.76105
[31] Xiao, F.; Honma, Y.; Kono, K., A simple algebraic interface capturing scheme using hyperbolic tangent function, Int J Numer Methods Fluids, 48, 1023-1040, (2005) · Zbl 1072.76046
[32] Ii, S.; Sugiyama, K.; Takeuchi, S.; Takagi, S.; Matsumoto, Y.; Xiao, F., An interface capturing method with a continuous function: the THINC method with multi-dimensional reconstruction, J Comput Phys, 231, 2328-2358, (2012) · Zbl 1427.76205
[33] Nonomura, T.; Kitamura, K.; Fujii, K., A simple interface sharpening technique with a hyperbolic tangent function applied to compressible two-fluid modeling, J Comput Phys, 258, 95-117, (2014) · Zbl 1349.76514
[34] Van Leer, B., Towards the ultimate conservative difference scheme. V. A second-order sequel to godunov’s method, J Comput Phys, 32, 101-136, (1979) · Zbl 1364.65223
[35] Van Albada, G. D.; Van Leer, B.; Roberts, W. W., A comparative study of computational methods in cosmic gas dynamics, Astron Astrophys, 108, 76-84, (1982) · Zbl 0492.76117
[36] Gottlieb, S.; Shu, C.-W., Total variation diminishing Runge-Kutta schemes, Math Comput, 67, 73-85, (1998) · Zbl 0897.65058
[37] Kitamura, K.; Roe, P.; Ismail, F., Evaluation of Euler fluxes for hypersonic flow computations, AIAA J, 47, 44-53, (2009)
[38] Stuhmiller, J., The influence of interfacial pressure forces on the character of two-phase flow model equations, Int J Multiphase Flow, 3, 551-560, (1977) · Zbl 0368.76085
[39] Chang C-H, Sushchikh S, Nguyen L, Liou M-S, Theofanous T. Hyperbolicity, discontinuities, and numerics of the two-fluid model. In: 5th Joint ASME/JSME fluids engineering summer conference. American Society of Mechanical Engineers, Fluid Engineering Div., Paper FEDSM2007-37338; 2007.
[40] Harlow F, Amsden A. Fluid dynamics. Technical Report LA-4700. Los Alamos National Laboratory; 1971. · Zbl 0221.76011
[41] Jolgam S, Ballil A, Nowakowski A, Nicolleau F. On equations of state for simulations of multiphase flows. In: Proc world congress on engineering 2012, vol. III. London, UK. WCE 2012; July 4-6, 2012.
[42] Glaister, P., An approximate linearised Riemann solver for the Euler equation for real gases, J Comput Phys, 92, 273-295, (1991)
[43] Morin, A.; Flatten, T.; Munkejord, S. T., A roe scheme for a compressible six-equation two-fluid model, Int J Numer Meth Fluids, 72, 4, 478-504, (2013) · Zbl 1455.76129
[44] Terashima, H.; Kawai, S.; Yamanishi, N., High-resolution numerical method for supercritical flows with large density variations, AIAA J, 49, 12, 2658-2672, (2011)
[45] Terashima, H.; Tryggvason, G., A front-tracking method with projected interface conditions for compressible multi-fluid flows, Comput Fluids, 39, 1804-1814, (2010) · Zbl 1245.76113
[46] Chen, H., Two-dimensional simulation of stripping breakup of a water droplet, AIAA J, 46, 5, 1135-1143, (2008)
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