Choice of measure source terms in interface coupling for a model problem in gas dynamics.

International audienceThis paper is devoted to the mathematical and numerical analysis of a coupling procedure for one-dimensional Euler systems. The two systems have different closure laws and are coupled through a thin fixed interface. Following the work of [5], we propose to couple these systems by a bounded vector-valued Dirac measure, concentrated at the coupling interface, which in the applications may have a physical meaning. We show that the proposed framework allows to control the coupling conditions and we propose an approximate Riemann solver based on a relaxation approach preserving equilibrium solutions of the coupled problem. Numerical experiments in constrained optimization problems are then presented to assess the performances of the present method. 1. Introduction The study of large-scale and complex problems exhibiting a wide range of physical space and time scales (see for instance [62, 35, 14]), usually requires separate solvers adapted to the resolution of specific scales. This is the case of many industrial flows. Let us quote, for example, the numerical simulation of two-phase flows applied to the burning liquid oxygen-hydrogen gas in rocket engines [58]. This kind of flow contains both separated and dispersed two-phase flows, due to atomization and evaporation phenomena. This requires appropriate models and solvers for separated and dispersed phases that have to be appropriately coupled. Another example concerns turbomachine flows which can be modeled by the Euler equations of gas dynamics with different closure laws between the stages of the turbine, where the conditions of temperature and pressure are strongly heterogeneous. The coupling of these different systems is thus necessary to give a complete description of the flow inside the whole turbine. The method of interface coupling allows to represent the evolution of such flows, where different models are separated by fixed interfaces. First, coupling conditions are specified at the interface to exchange information between the systems. The definition of transmission conditions generally results from physical consideration, e.g. the conservation or the continuity of given variables. Then, the transmission conditions are represented at the discrete level. The study of interface coupling for nonlinear hyperbolic systems has received attention for several years. In [43], the authors study the scalar case from both mathematical and numerical points of view

An entropy stable high-order discontinuous Galerkin spectral element method for the Baer-Nunziato two-phase flow model

International audienceIn this work we propose a high-order discretization of the Baer-Nunziato two-phase flow model (Baer and Nunziato (1986) [5]) with closures for interface velocity and pressure adapted to the treatment of discontinuous solutions, and stiffened gas equations of states. We use the discontinuous Galerkin spectral element method (DGSEM), based on collocation of quadrature and interpolation points (Kopriva and Gassner (2010) [47]). The DGSEM uses summation-by-parts (SBP) operators in the numerical quadrature for approximating the integrals over discretization elements (Carpenter et al. (2014) [10]; Gassner et al. (2016) [32]). Here, we build upon the framework provided in (Renac (2019) [55]) for nonconservative hyperbolic systems to modify the integration over cell elements using the SBP operators and replace the physical fluxes with entropy conservative fluctuation fluxes from Castro et al. (2013) [12], while we derive entropy stable numerical fluxes applied at interfaces. This allows to prove a semi-discrete inequality for the cell-averaged physical entropy, while keeping high-order accuracy. The design of the numerical fluxes also formally preserves the kinetic energy at the discrete level. High-order integration in time is performed using strong stability-preserving Runge-Kutta schemes and we propose conditions on the numerical parameters for the positivity of the cell-averaged void fraction and partial densities. The positivity of the cell-averaged solution is extended to nodal values by the use of an a posteriori limiter. The high-order accuracy, nonlinear stability, and robustness of the present scheme are assessed through several numerical experiments in one and two space dimensions

Adjoint approximation of nonlinear hyperbolic systems with non-conservative products

International audienceWe consider the approximation of adjoint-based derivatives for discontinuous solutions of the Cauchy problem associated to one-dimensional nonlinear non-conservative hyperbolic systems. We first derive the adjoint equations in strong form with a discontinuous primal solution together with the associated jump relations across the discontinuity. The adjoint solution may be discontinuous at the discontinuity in contrast to the case of conservative systems. Then, we consider first-order finite volume (FV) approximations to the primal problem and show that, using the Volpert path family of schemes, the discrete adjoint solution is consistent with the strong form adjoint solution. Numerical experiments are shown for a nonlinear 2 × 2 system with a genuinely nonlinear (GNL) field and a linearly degenerate (LD) field associated to the non-conservative product

Nonequilibrium Radiative Hypersonic Flows: Aerospace Applications

International audienceHyperenthalpic flows are encountered when spatial vehicules reenter the atmosphere (Anderson 1989) or in some astrophysical situations as in envelopes of cool pulsating stars (Lafon 1991). In reentry applications, a bow shock is created at the front of the vehicule. The plasma in the shock layer is highly collisional and the radiative heat flux is of the same order of magnitude as the convective heat flux. It is then necessary to take into account the coupling between aerodynamics and radiation.For high mach numbers, electronic collisional processes are out of equilibrium, and each atomic electronic level has to be considered as a distinct chemical species. The structure of the system is globally non-linear and the coupling is taken into account by mass conservation, energy exchange, and radiation-matter interaction. The radiative transfer also depends on atomic and molecular spectra in conditions of nonequilibrium for which cross sections and reaction rates are not well known and difficult to calculate

Modelisation de l'interaction particules-ecoulement dans un ecoulement turbulent

SIGLECNRS T Bordereau / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

A Roe-type linerazation for the Euler equations for weakly ionized multi-component and multi-temperature gas

Communication to : AIAA 12th CFD Conference, San Diego, CA (USA), June 19-22, 1995Available at INIST (FR), Document Supply Service, under shelf-number : 22419, issue : a.1995 n.109 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueSIGLEFRFranc

Methodes de decentrement hybrides pour la simulation d'ecoulements en desequilibre thermique et chimique

Communication to : 77th Fluid dynamics panel meeting and symposium on 'Progress and challenges in CFD methods and algorithms', Seville (Espagne), 2-5 octobre 1995SIGLEAvailable at INIST (FR), Document Supply Service, under shelf-number : 22419, issue : a.1995 n.139 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Methodes de decentrement hybrides pour la simulation d'ecoulements en desequilibre thermique et chimique

Communication to : 77th Fluid dynamics panel meeting and symposium on 'Progress and challenges in CFD methods and algorithms', Seville (Espagne), 2-5 octobre 1995SIGLEAvailable at INIST (FR), Document Supply Service, under shelf-number : 22419, issue : a.1995 n.139 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc