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.

Una codificación prefija para un idioma artificial

This work focuses in the formal and technical analysis of some aspects of a constructed language. As a first part of the work, a possible coding for the language will be studied, emphasizing the pre x coding, for which an extension of the Hu man algorithm from binary to n-ary will be implemented. Because of that in the language we can't know a priori the frequency of use of the words, a study will be done and several strategies will be proposed for an open words system, analyzing previously the existing number of words in current natural languages. As a possible upgrade of the coding, we'll take also a look to the synchronization loss problem, as well as to its solution: the self-synchronization, a t-codes study with the number of possible words for the language, as well as other alternatives. Finally, and from a less formal approach, several applications for the language have been developed: A voice synthesizer, a speech recognition system and a system font for the use of the language in text processors. For each of these applications, the process used for its construction, as well as the problems encountered and still to solve in each will be detailed.