All-regime Lagrangian-Remap numerical schemes for the gas dynamics equations. Applications to the large friction and low Mach coefficients

In this talk, we propose an all regime Lagrange-Projection like numerical scheme for the gas dynamics equations. By all regime, we mean that the numerical scheme is able to compute accurate approximate solutions with an under-resolved discretization with respect to the Mach number M, i.e. such that the ratio between the Mach number M and the mesh size or the time step is small with respect to 1. The key idea is to decouple acoustic and transport phenomenon and then alter the numerical flux in the acoustic approximation to obtain a uniform truncation error in term of M. This modified scheme is conservative and endowed with good stability properties with respect to the positivity of the density and the internal energy. A discrete entropy inequality under a condition on the modification is obtained thanks to a reinterpretation of the modified scheme in the Harten Lax and van Leer formalism. A natural extension to multi-dimensional problems discretized over unstructured mesh is proposed. Then a simple and efficient semi implicit scheme is also proposed. The resulting scheme is stable under a CFL condition driven by the (slow) material waves and not by the (fast) acoustic waves and so verifies the all regime property. Numerical evidences are proposed and show the ability of the scheme to deal with tests where the flow regime may vary from low to high Mach values.

Implementation of the CDM model to the analisys of the hotel sector

The main aim of this study was to determine the impact of innovation on productivity in service sector companies — especially those in the hospitality sector — that value the reduction of environmental impact as relevant to the innovation process. We used a structural analysis model based on the one developed by Crépon, Duguet, and Mairesse (1998). This model is known as the CDM model (an acronym of the authors’ surnames). These authors developed seminal studies in the field of the relationships between innovation and productivity (see Griliches 1979; Pakes and Grilliches 1980). The main advantage of the CDM model is its ability to integrate the process of innovation and business productivity from an empirical perspective.