A Robust Entropy-Satisfying Finite Volume Scheme for the Isentropic Baer-Nunziato Model
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In this article, an approximate Riemann solver for the isentropic Baer−Nunziato two-phase flow model is proposed, which is able to cope with arbitrarily small values of the statistical phase fractions.Abstract:
We construct an approximate Riemann solver for the isentropic Baer−Nunziato two-phase flow model, that is able to cope with arbitrarily small values of the statistical phase fractions The solver relies on a relaxation approximation of the model for which the Riemann problem is exactly solved for subsonic relative speeds In an original manner, the Riemann solutions to the linearly degenerate relaxation system are allowed to dissipate the total energy in the vanishing phase regimes, thereby enforcing the robustness and stability of the method in the limits of small phase fractions The scheme is proved to satisfy a discrete entropy inequality and to preserve positive values of the statistical fractions and densities The numerical simulations show a much higher precision and a more reduced computational cost (for comparable accuracy) than standard numerical schemes used in the nuclear industry Finally, two test-cases assess the good behavior of the scheme when approximating vanishing phase solutionsread more
Citations
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A well-balanced scheme to capture non-explicit steady states in the Euler equations with gravity
TL;DR: In this paper, a numerical discretization of the compressible Euler equations with a gravitational potential is presented, which is a finite volume method, whose Riemann solver is approximated by a so-called relaxation RiemANN solution that takes all hydrostatic equilibria into account.
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A positive and entropy-satisfying finite volume scheme for the Baer-Nunziato model
TL;DR: 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.
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Validation of a two-fluid model on unsteady liquid–vapor water flows
TL;DR: In this paper, a two-fluid two-phase flow model was validated in some highly unsteady situations involving strong rarefaction waves and shocks in water-vapor flows.
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HLLC-type Riemann solver with approximated two-phase contact for the computation of the Baer-Nunziato two-fluid model
TL;DR: A new HLLC-type Riemann solver is built based on the solver proposed by Tokareva & Toro, and the key idea lies in an approximation of the two-phase contact discontinuity of the Baer–Nunziato model, which allows to bypass the resolution of a non-linear equation based on those Riem Mann invariants.
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Entropy stable DGSEM for nonlinear hyperbolic systems in nonconservative form with application to two-phase flows
TL;DR: This work considers the discretization of nonlinear hyperbolic systems in nonconservative form with the high-order discontinuous Galerkin spectral element method (DGSEM), and presents a general framework for the design of such schemes that satisfy a semi-discrete entropy inequality for a given convex entropy function at any approximation order.
References
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On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws
TL;DR: This paper reviews some of the recent developments in upstream difference schemes through a unified representation, in order to enable comparison between the various schemes.
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Numerical Approximation of Hyperbolic Systems of Conservation Laws
TL;DR: In this paper, the authors define and define nonlinear hyperbolic systems in one space dimension and define finite difference schemes for one-dimensional systems in the case of multidimensional systems.
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A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials
Melvin R. Baer,J.W. Nunziato +1 more
TL;DR: In this article, a two-phase mixture theory is presented which describes the deflagration-to-detonation transition (DDT) in reactive granular materials, based on the continuum theory of mixtures formulated to include the compressibility of all phases and the compaction behavior of the granular material.
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A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows
Richard Saurel,Rémi Abgrall +1 more
TL;DR: A new model and a solution method for two-phase compressible flows is proposed that provides reliable results, is able to compute strong shock waves, and deals with complex equations of state.
Journal ArticleDOI
Hyperbolic conservation laws with stiff relaxation terms and entropy
TL;DR: In this paper, the limiting behavior of systems of hyperbolic conservation laws with stiff relaxation terms was studied and the convergence to the reduced dynamics for the 2 × 2 case was studied.
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