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Hybrid central-upwind schemes for numerical resolutionof two-phase flows

Published online by Cambridge University Press:  15 April 2005

Steinar Evje  and
Tore Flåtten
Steinar Evje
Affiliation:
RF-Rogaland Research, Prof. Olav Hanssensvei 15, Stavanger, Norway. steinar.evje@rf.no; t.h.flatten@cma.uio.no
Tore Flåtten
Affiliation:
RF-Rogaland Research, Prof. Olav Hanssensvei 15, Stavanger, Norway. steinar.evje@rf.no; t.h.flatten@cma.uio.no
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Abstract

In this paper we present a methodology for constructing accurateand efficient hybrid central-upwind (HCU) type schemes forthe numerical resolution of a two-fluid model commonly used by thenuclear and petroleum industry. Particularly, we propose a methodwhich does not make use of any information about theeigenstructure 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 evolutionequation which describes how pressure evolves in time. By applyinga quasi-staggered Lax-Friedrichs type discretization for thispressure equation together with a Modified Lax-Friedrich typediscretization of the convective terms, we obtain a central typescheme which allows to cope with the nonlinearity (nonlinearpressure waves) of the two-fluid model in a robust manner.Then, in order to obtain an accurate resolution of mass fronts, weemploy a modification of the convective mass fluxes by hybridizingthe central type mass flux components with upwind type components.This hybridization is based on a splitting of the mass fluxes intocomponents corresponding to the pressure and volume fractionvariables, recovering an accurate resolution of a contactdiscontinuity. In the numerical simulations, the resulting HCU scheme givesresults comparable to an approximate Riemann solver while beingsuperior in efficiency. Furthermore, the HCU scheme yields betterrobustness than other popular Riemann-free upwind schemes.

Keywords

Two-phase flowtwo-fluid modelhyperbolic system of conservationlawscentral discretizationupwind discretizationpressureevolution equationhybrid scheme.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 2 , March 2005 , pp. 253 - 273
Copyright
© EDP Sciences, SMAI, 2005

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References

Abgrall, R., How to prevent pressure oscillations in multicomponent flow calculations. J. Comput. Phys. 125 (1996) 150–160. CrossRef
Barre, F. et al., The CATHARE code strategy and assessment. Nucl. Eng. Des. 124 (1990) 257–284. CrossRef
K.H. Bendiksen, D. Malnes, R. Moe and S. Nuland, The dynamic two-fluid model OLGA: Theory and application, in SPE Prod. Eng. 6 (1991) 171–180.
Coquel, F., El Amine, K., Godlewski, E., Perthame, B. and Rascle, P., A numerical method using upwind schemes for the resolution of two-phase flows. J. Comput. Phys. 136 (1997) 272–288. CrossRef
Cortes, J., Debussche, A. and Toumi, I., A density perturbation method to study the eigenstructure of two-phase flow equation systems. J. Comput. Phys. 147 (1998) 463–484. CrossRef
Evje, S. and Fjelde, K.K., Hybrid flux-splitting schemes for a two-phase flow model. J. Comput. Phys. 175 (2002) 674–701. CrossRef
Evje, S. and Fjelde, K.K., On a rough ausm scheme for a one-dimensional two-phase flow model. Comput. Fluids 32 (2003) 1497–1530. CrossRef
Evje, S. and Flåtten, T., Hybrid flux-splitting schemes for a common two-fluid model. J. Comput. Phys. 192 (2003) 175–210. CrossRef
S. Evje and T. Flåtten, Weakly implicit numerical schemes for a two-fluid model. SIAM J. Sci. Comput., accepted.
T. Flåtten, Hybrid flux-splitting schemes for numerical resolution of two-phase flows. Dr.ing.-thesis, Norwegian University of Science and Technology (2003) 114.
M. Larsen, E. Hustvedt, P. Hedne and T. Straume, PeTra: A novel computer code for simulation of slug flow, in SPE Annual Technical Conference and Exhibition, SPE 38841 (October 1997) 1–12.
Liou, M.-S., A sequel to AUSM: AUSM(+). J. Comput. Phys. 129 (1996) 364–382. CrossRef
Niu, Y.Y., Simple conservative flux splitting for multi-component flow calculations. Num. Heat Trans. 38 (2000) 203–222. CrossRef
Niu, Y.Y., Advection upwinding splitting method to solve a compressible two-fluid model. Internat. J. Numer. Methods Fluids 36 (2001) 351–371. CrossRef
Paillère, H., Corre, C. and Cascales, J.R.G., On the extension of the AUSM+ scheme to compressible two-fluid models. Comput. Fluids 32 (2003) 891–916. CrossRef
Ransom, V.H., Numerical bencmark tests. Multiphase Sci. Tech. 3 (1987) 465-473. CrossRef
V.H. Ransom et al., RELAP5/MOD3 Code Manual, NUREG/CR-5535, Idaho National Engineering Laboratory (1995).
Saurel, R. and Abgrall, R., A multiphase Godunov method for compressible multifluid and multiphase flows. J. Comput. Phys. 150 (1999) 425–467. CrossRef
Tadmor, E., Numerical viscosity and the entropy condition for conservative difference schemes. Math. Comp. 168 (1984) 369–381. CrossRef
Tiselj, I. and Petelin, S., Modelling of two-phase flow with second-order accurate scheme. J. Comput. Phys. 136 (1997) 503–521. CrossRef
Toumi, I., An upwind numerical method for two-fluid two-phase flow models. Nuc. Sci. Eng. 123 (1996) 147–168. CrossRef
Toumi, I. and Kumbaro, A., An approximate linearized riemann solver for a two-fluid model. J. Comput. Phys. 124 (1996) 286–300. CrossRef
Trapp, J.A. and Riemke, R.A., A nearly-implicit hydrodynamic numerical scheme for two-phase flows. J. Comput. Phys. 66 (1986) 62–82. CrossRef
Wada, Y. and Liou, M.-S., An accurate and robust flux splitting scheme for shock and contact discontinuities. SIAM J. Sci. Comput. 18 (1997) 633–657. CrossRef