Prandtl number effects in MRT Lattice Boltzmann models for shocked and unshocked compressible fluids

For compressible fluids under shock wave reaction, we have proposed two Multiple-Relaxation-Time (MRT) Lattice Boltzmann (LB) models [F. Chen, et al, EPL \textbf{90} (2010) 54003; Phys. Lett. A \textbf{375} (2011) 2129.]. In this paper, we construct a new MRT Lattice Boltzmann model which is not only for the shocked compressible fluids, but also for the unshocked compressible fluids. To make the model work for unshocked compressible fluids, a key step is to modify the collision operators of energy flux so that the viscous coefficient in momentum equation is consistent with that in energy equation even in the unshocked system. The unnecessity of the modification for systems under strong shock is analyzed. The model is validated by some well-known benchmark tests, including (i) thermal Couette flow, (ii) Riemann problem, (iii) Richtmyer-Meshkov instability. The first system is unshocked and the latter two are shocked. In all the three systems, the Prandtl numbers effects are checked. Satisfying agreements are obtained between new model results and analytical ones or other numerical results.Comment: 17 pages, 8 figure

Fluid Flow and Heat Transfer in Cellular Solids

To determine the characteristics and properties of cellular solids for an application, and to allow a systematic practical use by means of correlations and modelling approaches, we perform experimental investigations and develop numerical methods. In view of coupled multi-physics simulations, we employ the phase-field method. Finally, the applicability is demonstrated exemplarily for open-cell metal foams, providing qualitative and quantitative comparison with experimental data

Fluid Flow and Heat Transfer in Cellular Solids

To determine the characteristics and properties of cellular solids for an application, and to allow a systematic practical use by means of correlations and modelling approaches, we perform experimental investigations and develop numerical methods. In view of coupled multi-physics simulations, we employ the phase-field method. Finally, the applicability is demonstrated exemplarily for open-cell metal foams, providing qualitative and quantitative comparison with experimental data