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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.

Information

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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