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.

Applications of synchrotron x-ray powder diffraction in hydrated cements: high-resolution and high-pressure studies

The main aim of this study is to apply synchrotron radiation techniques for the study of hydrated cement pastes. In particular, the tetracalcium aluminoferrite phase, C4AF in cement nomenclature, is the major iron-containing phase in Ordinary Portland Cement (OPC) and in iron rich belite calcium sulfoaluminate cements. In a first study, the hydration mechanism of pure tetracalcium aluminoferrite phase with water-to-solid ratio of 1.0 has been investigated by HR-SXRPD (high resolution synchrotron X-ray powder diffraction). C4AF in the presence of water hydrates to form mainly an iron-containing hydrogarnet-type (katoite) phase, C3A0.84F0.16H6, as single crystalline phase. Its crystal structure and stoichiometry were determined by the Rietveld method and the final disagreement factors were RWP=8.1% and RF=4.8% [1]. As the iron content in the product is lower than that in C4AF, it is assumed that part of the iron also goes to an amorphous iron rich gel, like the hydrated alumina-type gel, as hydration proceeds. Further results from the high-resolution study will be discussed. In a second study, the behavior of pure and iron-containing katoites (C3AH6 and C3A0.84F0.16H6) under pressure have been analyzed by SXRPD using a diamond anvil cell (DAC) and then their bulk moduli were determined. The role of the pressure transmitting medium (PTM) has also been studied. In this case, silicone oil as well as methanol/ethanol mixtures have been used as PTM. Some “new peaks” were detected in the pattern for C3A0.84F0.16H6 as pressure increases, when using ethanol/methanol as PTM. These new peaks were still present at ambient pressure after releasing the applied pressure. They may correspond to crystalline nordstrandite or doyleite from the crystallization of amorphous aluminium hydroxide. The results from the high-pressure study will also be discussed.