We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation.
For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound are more » also proven to be maintained by the numerical scheme. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in for the isentropic Baer–Nunziato model and consequently inherits its main properties.
We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer–Nunziato two-phase flow model. (INL), Idaho Falls, ID (United States) Sponsoring Org.: USDOE Office of Nuclear Energy (NE) OSTI Identifier: 1557597 Alternate Identifier(s): OSTI ID: 1776268 Report Number(s): INL/JOU-18-52250-Rev000 Journal ID: ISSN 0045-7825 Grant/Contract Number: AC07-05ID14517 Resource Type: Accepted Manuscript Journal Name: Computer Methods in Applied Mechanics and Engineering Additional Journal Information: Journal Volume: 354 Journal Issue: C Journal ID: ISSN 0045-7825 Publisher: Elsevier Country of Publication: United States Language: English Subject: 97 MATHEMATICS AND COMPUTING 42 ENGINEERING variable cross-section flows (temporal and spatial) Baer-Nunziato model Finite Volume ALE formulation pipe network junction flexible = , Publication Date: Mon Jun 17 00:00: Research Org.: Idaho National Lab. Paris-Saclay, Palaiseau (France) Alternative Energies and Atomic Energy Commission (CEA), Saclay (France) Paris-Saclay, Palaiseau (France) EDF R&D, ERMES, Palaiseau (France) Lastly, the proposed scheme is then assessed on a variety of shock-tubes and other transient flow problems and experiments demonstrating its capability to resolve such problems efficiently, accurately and robustly. In addition, the fluid–structure interaction of compressible fluid flowing in flexible pipes is also considered. The present approach can also deal with general Equations Of State. The proposed method makes it possible to avoid the use of an iterative procedure for the solution of the junction problem. In particular, focus is given to the numerical treatment of abrupt changes in area and to networks wherein several pipelines are connected at junctions. In addition, proper approximations of the non-conservative terms are proposed to consider jumps of volume fraction as well as jumps of cross-section in order to respect uniform pressure and velocity profiles preservation. The present FV approach is the extension of the method proposed in Daude and Galon (2018) in the context of the Euler equations to the Baer–Nunziato model.
A novel Finite-Volume scheme for the numerical computations of compressible two-phase flows in pipelines is proposed for the fully non-equilibrium Baer–Nunziato model.
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