Many problems in fluid mechanics and material sciences deal with liquid-vapour flows. In these flows, the ideal gas assumption is not accurate and the van der Waals equation of state is usually used. This equation of state is non-convex and causes the solution domain to have two hyperbolic regions separated by an elliptic region. Therefore, the governing equations of these flows have a mixed elliptic-hyperbolic nature. Numerical oscillations usually appear with standard finite-difference space discretization schemes, and they persist when the order of accuracy of the semi-discrete scheme is increased. In this study, we propose to use a Chebyshev pseudospectral method for solving the governing equations. A comparison of the results of this method with very high-order (up to tenth-order accurate) finite difference schemes is presented, which shows that the proposed method leads to a lower level of numerical oscillations than other high-order finite difference schemes, and also does not exhibit fast-traveling packages of short waves which are usually observed in high-order finite difference methods. The proposed method can thus successfully capture various complex regimes of waves and phase transitions in both elliptic and hyperbolic regimes

Many problems in fluid mechanics and material sciences deal with liquid-vapour flows. In these flows, the ideal gas assumption is not accurate and the van der Waals equation of state is usually used. This equation of state is non-convex and causes the solution domain to have two hyperbolic regions separated by an elliptic region. Therefore, the governing equations of these flows have a mixed elliptic-hyperbolic nature. Numerical oscillations usually appear with standard finite-difference space discretization schemes, and they persist when the order of accuracy of the semi-discrete scheme is increased. In this study, we propose to use a Chebyshev pseudospectral method for solving the governing equations. A comparison of the results of this method with very high-order (up to tenth-order accurate) finite difference schemes is presented, which shows that the proposed method leads to a lower level of numerical oscillations than other high-order finite difference schemes, and also does not exhibit fast-traveling packages of short waves which are usually observed in high-order finite difference methods. The proposed method can thus successfully capture various complex regimes of waves and phase transitions in both elliptic and hyperbolic regimes

Many problems in fluid mechanics and material sciences deal with liquid-vapour flows. In these flows, the ideal gas assumption is not accurate and the van der Waals equation of state is usually used. This equation of state is non-convex and causes the solution domain to have two hyperbolic regions separated by an elliptic region. Therefore, the governing equations of these flows have a mixed elliptic-hyperbolic nature. Numerical oscillations usually appear with standard finite-difference space discretization schemes, and they persist when the order of accuracy of the semi-discrete scheme is increased. In this study, we propose to use a Chebyshev pseudospectral method for solving the governing equations. A comparison of the results of this method with very high-order (up to tenth-order accurate) finite difference schemes is presented, which shows that the proposed method leads to a lower level of numerical oscillations than other high-order finite difference schemes, and also does not exhibit fast-traveling packages of short waves which are usually observed in high-order finite difference methods. The proposed method can thus successfully capture various complex regimes of waves and phase transitions in both elliptic and hyperbolic regimes

Many problems in fluid mechanics and material sciences deal with liquid-vapour flows. In these flows, the ideal gas assumption is not accurate and the van der Waals equation of state is usually used. This equation of state is non-convex and causes the solution domain to have two hyperbolic regions separated by an elliptic region. Therefore, the governing equations of these flows have a mixed elliptic-hyperbolic nature. Numerical oscillations usually appear with standard finite-difference space discretization schemes, and they persist when the order of accuracy of the semi-discrete scheme is increased. In this study, we propose to use a Chebyshev pseudospectral method for solving the governing equations. A comparison of the results of this method with very high-order (up to tenth-order accurate) finite difference schemes is presented, which shows that the proposed method leads to a lower level of numerical oscillations than other high-order finite difference schemes, and also does not exhibit fast-traveling packages of short waves which are usually observed in high-order finite difference methods. The proposed method can thus successfully capture various complex regimes of waves and phase transitions in both elliptic and hyperbolic regimes

Les enjeux de réduction des consommations d’énergie, d’estimation de la durabilité ainsi que l’évolution des pratiques constructives et réglementaires génèrent une augmentation significative du niveau de détail exigé dans la simulation des phénomènes physiques du Génie Civil pour une prédiction fiable du comportement des ouvrages. Le bâtiment est le siège de phénomènes couplés multi-échelles, entre le microscopique (voire le nanoscopique) et le macroscopique, impliquant des études de couplages complexes entre matériaux, à l’instar des phénomènes de sorption-désorption qui influent sur la résistance mécanique, les transferts de masse, la conductivité, le stockage d’énergie ou la durabilité d’un ouvrage. Les méthodes numériques appliquées permettent de résoudre certains de ces problèmes en ayant recours aux techniques de calcul multi-grilles, de couplage multi-échelles ou de parallélisation massive afin de réduire substantiellement les temps de calcul. Dans le présent travail, qui traite de plusieurs simulations ayant trait à la physique du bâtiment, nous nous intéressons à la pertinence d’utilisation de la méthode "Lattice Boltzmann". Il s’agit d’une méthode numérique construite sur une grille – d’où l’appellation de lattice – dite "mésoscopique" qui, à partir d’un raisonnement de thermodynamique statistique sur le comportement d’un groupes de particules microscopiques de fluide, permet d’obtenir une extrapolation consistante vers son comportement macroscopique. Après une étude les avantages comparés de la méthode et sur le comportement oscillatoire qu'elle exhibe dans certaines configurations, on présente :- une application au calcul des propriétés diffusives homogénéisée des matériaux cimentaires en cours d'hydratation, par résolution sur le cluster du LMT.- une application à l'énergétique du bâtiment avec la comportement d'une paroi solaire dynamique, dont le calcul a été porté sur carte graphique afin d'en évaluer le potentiel. / Reducing building energy consumption and estimating the durability of structures are ongoing challenges in the current regulatory framework and construction practice. They suppose a significant increase of the level of detail for simulating the physical phenomena of Civil Engineering to achieve a reliable prediction of structures.Building is the centre of multi-scale, coupled phenomena ranging from the micro (or even nano) to the macro-scale, thus implying complex couplings between materials such as sorption-desorption process which influences the intrinsic properties of matter such as mechanical resistance, mass transfer, thermal conductivity, energy storage or durability.Applied numerical methods allow for the resolution of some of these problems by using multi-grid computing, multi-scale coupling or massive parallelisation in order to substantially reduce the computing time.The present work is intended to evaluate the suitability of the “lattice Boltzmann method” applied to several applications in building physics. This numerical method, said to be “mesoscopic”, starts from the thermodynamic statistical behaviour of a group of fluid particles, mimicking the macroscopic behaviour thanks to a consistent extrapolation across the scales.After having studied the comparative advantages of the method and the oscillatory behaviour it displays under some circumstances, we present - An application to the diffusive properties of cementitious materials during hydration via numerical homogenization and cluster-computing numerical campaign - An application to building energy with the modeling of a solar active wall in forced convection simulated on a graphical processing unit.