In this paper we present a methodology for constructing accurate and efficient hybrid central-upwind (HCU) type schemes for the numerical resolution of a two-fluid model commonly used by the nuclear and petroleum industry. Particularly, we propose a method which does not make use of any information about the eigenstructure of the jacobian matrix of the model. The two-fluid model possesses a highly nonlinear pressure law. From the mass conservation equations we develop an evolution equation which describes how pressure evolves in time. By applying a quasi-staggered Lax-Friedrichs type discretization for this pressure equation together with a Modified Lax-Friedrich type discretization of the convective terms, we obtain a central type scheme which allows to cope with the nonlinearity (nonlinear pressure waves) of the two-fluid model in a robust manner. Then, in order to obtain an accurate resolution of mass fronts, we employ a modification of the convective mass fluxes by hybridizing the central type mass flux components with upwind type components. This hybridization is based on a splitting of the mass fluxes into components corresponding to the pressure and volume fraction variables, recovering an accurate resolution of a contact discontinuity. In the numerical simulations, the resulting HCU scheme gives results comparable to an approximate Riemann solver while being superior in efficiency. Furthermore, the HCU scheme yields better robustness than other popular Riemann-free upwind schemes.
Mots-clés : two-phase flow, two-fluid model, hyperbolic system of conservation laws, central discretization, upwind discretization, pressure evolution equation, hybrid scheme
@article{M2AN_2005__39_2_253_0,
author = {Evje, Steinar and Fl\r{a}tten, Tore},
title = {Hybrid central-upwind schemes for numerical resolution of two-phase flows},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {253--273},
publisher = {EDP-Sciences},
volume = {39},
number = {2},
year = {2005},
doi = {10.1051/m2an:2005011},
mrnumber = {2143949},
zbl = {1130.76057},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2005011/}
}
TY - JOUR AU - Evje, Steinar AU - Flåtten, Tore TI - Hybrid central-upwind schemes for numerical resolution of two-phase flows JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2005 SP - 253 EP - 273 VL - 39 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2005011/ DO - 10.1051/m2an:2005011 LA - en ID - M2AN_2005__39_2_253_0 ER -
%0 Journal Article %A Evje, Steinar %A Flåtten, Tore %T Hybrid central-upwind schemes for numerical resolution of two-phase flows %J ESAIM: Modélisation mathématique et analyse numérique %D 2005 %P 253-273 %V 39 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2005011/ %R 10.1051/m2an:2005011 %G en %F M2AN_2005__39_2_253_0
Evje, Steinar; Flåtten, Tore. Hybrid central-upwind schemes for numerical resolution of two-phase flows. ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 2, pp. 253-273. doi : 10.1051/m2an:2005011. http://www.numdam.org/articles/10.1051/m2an:2005011/
[1] , How to prevent pressure oscillations in multicomponent flow calculations. J. Comput. Phys. 125 (1996) 150-160. | Zbl
[2] et al., The CATHARE code strategy and assessment. Nucl. Eng. Des. 124 (1990) 257-284.
[3] ,, and, The dynamic two-fluid model OLGA: Theory and application, in SPE Prod. Eng. 6 (1991) 171-180.
[4] ,,, and, A numerical method using upwind schemes for the resolution of two-phase flows. J. Comput. Phys. 136 (1997) 272-288. | Zbl
[5] , and, A density perturbation method to study the eigenstructure of two-phase flow equation systems. J. Comput. Phys. 147 (1998) 463-484. | Zbl
[6] and, Hybrid flux-splitting schemes for a two-phase flow model. J. Comput. Phys. 175 (2002) 674-701.
[7] and, On a rough ausm scheme for a one-dimensional two-phase flow model. Comput. Fluids 32 (2003) 1497-1530. | Zbl
[8] and, Hybrid flux-splitting schemes for a common two-fluid model. J. Comput. Phys. 192 (2003) 175-210. | Zbl
[9] and, Weakly implicit numerical schemes for a two-fluid model. SIAM J. Sci. Comput., accepted. | MR
[10] , Hybrid flux-splitting schemes for numerical resolution of two-phase flows. Dr.ing.-thesis, Norwegian University of Science and Technology (2003) 114.
[11] ,, and, PeTra: A novel computer code for simulation of slug flow, in SPE Annual Technical Conference and Exhibition, SPE 38841 (October 1997) 1-12.
[12] , A sequel to AUSM: AUSM(+). J. Comput. Phys. 129 (1996) 364-382. | Zbl
[13] , Simple conservative flux splitting for multi-component flow calculations. Num. Heat Trans. 38 (2000) 203-222.
[14] , Advection upwinding splitting method to solve a compressible two-fluid model. Internat. J. Numer. Methods Fluids 36 (2001) 351-371. | Zbl
[15] , and, On the extension of the AUSM+ scheme to compressible two-fluid models. Comput. Fluids 32 (2003) 891-916. | Zbl
[16] , Numerical bencmark tests. Multiphase Sci. Tech. 3 (1987) 465-473.
[17] et al., RELAP5/MOD3 Code Manual, NUREG/CR-5535, Idaho National Engineering Laboratory (1995).
[18] and, A multiphase Godunov method for compressible multifluid and multiphase flows. J. Comput. Phys. 150 (1999) 425-467. | Zbl
[19] , Numerical viscosity and the entropy condition for conservative difference schemes. Math. Comp. 168 (1984) 369-381. | Zbl
[20] and, Modelling of two-phase flow with second-order accurate scheme. J. Comput. Phys. 136 (1997) 503-521. | Zbl
[21] , An upwind numerical method for two-fluid two-phase flow models. Nuc. Sci. Eng. 123 (1996) 147-168.
[22] and, An approximate linearized riemann solver for a two-fluid model. J. Comput. Phys. 124 (1996) 286-300. | Zbl
[23] and, A nearly-implicit hydrodynamic numerical scheme for two-phase flows. J. Comput. Phys. 66 (1986) 62-82. | Zbl
[24] and, An accurate and robust flux splitting scheme for shock and contact discontinuities. SIAM J. Sci. Comput. 18 (1997) 633-657. | Zbl
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