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International audienceThe multislope concept has been recently introduced in the literature to deal with MUSCL reconstructions on triangular and tetrahedral unstructured meshes in the finite volume cell-centered context. Dedicated scalar slopes are used to compute the interpolations on each face of a given element, in opposition to the monoslope methods in which a unique limited gradient is used. The multislope approach reveals less expensive and potentially more accurate than the classical gradient techniques. Besides, it may also help the robustness when dealing with hyperbolic systems involving complex solutions, with large discontinuities and high density ratios. However some important limitations on the mesh topology still have to be overcome with the initial multislope formalism. In this paper, a generalized multislope MUSCL method is introduced for cell-centered finite volume discretizations. The method is freed from constraints on the mesh topology, thereby operating on completely general unstructured meshes. Moreover optimal second-order accuracy is reached at the faces centroids. The scheme can be written with nonnegative coefficients, which makes it L∞L∞-stable. Special attention has also been paid to equip the reconstruction procedure with well-adapted dedicated limiters, potentially CFL-dependent. Numerical tests are provided to prove the ability of the method to deal with completely general meshes, while exhibiting second-order accuracy

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The present contribution lies on the high-frequency combustion instability issue occurring in liquid rocket engines, and focuses on subcritical operating conditions. Thanks to the development of high-performance computing and advanced numerical simulation codes, large-eddy simulation has become an essential analysis tool in the domain. Different unsteady numerical strategies exist to handle the wide range of time and length scales involved in two-phase flows related to subcritical operating conditions, but only a few are adapted to deal with reactive flows. What is more, most of them are developed without any consideration for possible acoustic effects on atomization processes while these may have a great impact on the stability of the engine. Therefore, the present contribution aims at evaluating the ability of one of these numerical strategies in particular to render acoustic effects on atomized liquid jets typical of what happens under unstable operating conditions. To do so, the numerical simulation of a non-reactive two-phase flow submitted to a transverse acoustic modulation is performed. Two cases are simulated, the first one with acoustic modulation, the jet lying in the vicinity of a transverse intensity anti-node, and the second one without any. In order to highlight the effect of acoustics on the liquid phase, the two cases are compared to one another as well as to experiments presented in the literature. The numerical strategy used in these simulations is based on the coupling between a diffuse interface method for the simulation of large liquid structures, and a kinetic-based Eulerian model for the description of droplets. It is found that the flattening of the liquid core under acoustic constraints is retrieved in the simulations. This flattening process thus induces a decrease of the liquid core length and an intensification of its stripping. The additional mass of liquid thus ripped from the liquid jet is transformed into droplets and the spray undergoes a drastic modification of its shape thanks to an appropriate primary atomization source term. Finally, periodic oscillations of droplets under the acoustic velocity are rendered thanks to the coupling between the gaseous phase and the spray through a drag source term. The numerical strategy thus appears adapted to deal with numerical simulations of coaxial two-phase flows under transverse acoustic modulation, in which the response of the gas, the liquid core and the spray are all linked to one another. This strategy can then be used for future numerical studies of high-frequency combustion instabilities.