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arXiv · 0803.2469

An entropy preserving finite-element/finite-volume pressure correction scheme for the drift-flux model

Laura Gastaldo·Raphaele Herbin·Jean-Claude Latché
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Abstract

We present in this paper a pressure correction scheme for the drift-flux 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 Darcy-like 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 drift-flux model. Numerical tests show a near-first-order convergence rate for the scheme, both in time and space, and confirm its stability.

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Laura Gastaldo, Raphaele Herbin, Jean-Claude Latché. 2008-03-17. An entropy preserving finite-element/finite-volume pressure correction scheme for the drift-flux model. https://arxiv.org/abs/0803.2469

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