Publications (7)0 Total impact
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ABSTRACT: We present in this paper a pressure correction scheme for the driftflux model combining finite element and finite volume discretizations, which is shown to enjoy essential stability features of the continuous problem: the scheme is conservative, the unknowns are kept within their physical bounds and, in the homogeneous case (i.e. when the drift velocity vanishes), the discrete entropy of the system decreases; in addition, when using for the drift velocity a closure law which takes the form of a Darcylike relation, the drift term becomes dissipative. Finally, the present algorithm preserves a constant pressure and a constant velocity through moving interfaces between phases. To ensure the stability as well as to obtain this latter property, a key ingredient is to couple the mass balance and the transport equation for the dispersed phase in an original pressure correction step. The existence of a solution to each step of the algorithm is proven; in particular, the existence of a solution to the pressure correction step is derived as a consequence of a more general existence result for discrete problems associated to the driftflux model. Numerical tests show a nearfirstorder convergence rate for the scheme, both in time and space, and confirm its stability.European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis. 01/2010; 44(2). 
Article: A discretization of phases mass balance in fractional step algorithms for the driftflux model}
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ABSTRACT: We address in this paper a parabolic equation used to model the phases mass balance in twophase flows, which differs from the mass balance for chemical species in compressible multicomponent flows by the addition of a nonlinear term of the form $\dive \rho \phi(y) \, u_r$, where $y$ is the unknown mass fraction, $\rho$ stands for the density, $\phi(\cdot)$ is a regular function such that $\phi(0)=\phi(1)=0$ and $u_r$ is a (nonnecessarily divergence free) velocity field. We propose a finitevolume scheme for the numerical approximation of this equation, with a discretization of the nonlinear term based on monotone flux functions \cite{eym00fin}. Under the classical assumption \cite{lar91how} that the discretization of the convection operator must be such that it vanishes for constant $y$, we prove the existence and uniqueness of the solution, together with the fact that it remains within its physical bounds, \ie\ within the interval $[0,1]$. Then this scheme is combined with a pressure correction method to obtain a semiimplicit fractionalstep scheme for the socalled driftflux model. To satisfy the abovementioned assumption, a specific timestepping algorithm with particular approximations for the density terms is developed. Numerical tests are performed to assess the convergence and stability properties of this scheme.01/2009;  [Show abstract] [Hide abstract]
ABSTRACT: We present in this paper a pressure correction scheme for the driftflux model combining finite element and finite volume discretizations, which is shown to enjoy essential stability features of the continuous problem: the scheme is conservative, the unknowns are kept within their physical bounds and, in the homogeneous case (i.e. when the drift velocity vanishes), the discrete entropy of the system decreases; in addition, when using for the drift velocity a closure law which takes the form of a Darcylike relation, the drift term becomes dissipative. Finally, the present algorithm preserves a constant pressure and a constant velocity through moving interfaces between phases. To ensure the stability as well as to obtain this latter property, a key ingredient is to couple the mass balance and the transport equation for the dispersed phase in an original pressure correction step. The existence of a solution to each step of the algorithm is proven; in particular, the existence of a solution to the pressure correction step is derived as a consequence of a more general existence result for discrete problems associated to the driftflux model. Numerical tests show a nearfirstorder convergence rate for the scheme, both in time and space, and confirm its stability.04/2008;  01/2008;
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ABSTRACT: We present in this paper a pressure correction scheme for barotropic compressible NavierStokes equations, which enjoys an unconditional stability property, in the sense that the energy and maximumprinciplebased a priori estimates of the continuous problem also hold for the discrete solution. The stability proof is based on two independent results for general finite volume discretizations, both interesting for their own sake: the L 2 stability of the discrete advection operator provided it is consistent, in some sense, with the mass balance and the estimate of the pressure work by means of the time derivative of the elastic potential. The proposed scheme is built in order to match these theoretical results, and combines a fractionalstep time discretization of pressurecorrection type to a space discretization associating low order nonconforming mixed finite elements and finite volumes. Numerical tests with an exact smooth solution show the convergence of the scheme.11/2007;  [Show abstract] [Hide abstract]
ABSTRACT: We present in this paper a class of schemes for the solution of the barotropic Navier Stokes equations. These schemes work on general meshes, preserve the stability properties of the continuous problem, irrespectively of the space and time steps, and boil down, when the Mach number vanishes, to discretizations which are standard (and stable) in the incompressible framework. Finally, we show that they are able to capture solutions with shocks to the Euler equations 
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2008–2009

Institut de Radioprotection et de Sûreté Nucléaire (IRSN)
Fontenay, ÎledeFrance, France
