A lattice Boltzmann method (LBM) with enhanced stability and accuracy is presented for various Hermite tensor-based lattice structures. The collision operator relies on a regularization step, which is here improved through a recursive computation of nonequilibrium Hermite polynomial coefficients. In addition to the reduced computational cost of this procedure with respect to the standard one, the recursive step allows to considerably enhance the stability and accuracy of the numerical scheme by properly filtering out second- (and higher-) order nonhydrodynamic contributions in under-resolved conditions. This is first shown in the isothermal case where the simulation of the doubly periodic shear layer is performed with a Reynolds number ranging from ${10}^4$ to ${10}^6$, and where a thorough analysis of the case at $\text{Re}=3\times {10}^4$ is conducted. In the latter, results obtained using both regularization steps are compared against the Bhatnagar-Gross-Krook LBM for standard (D2Q9) and high-order (D2V17 and D2V37) lattice structures, confirming the tremendous increase of stability range of the proposed approach. Further comparisons on thermal and fully compressible flows, using the general extension of this procedure, are then conducted through the numerical simulation of Sod shock tubes with the D2V37 lattice. They confirm the stability increase induced by the recursive approach as compared with the standard one.

Efficient numerical tools taking advantage of the ever increasing power of high-performance computers, become key elements in the fields of energy supply and transportation, not only from a purely scientific point of view, but also at the design stage in industry. Indeed, flow phenomena that occur in or around the industrial applications such as gas turbines or aircraft are still not mastered. In fact, most Computational Fluid Dynamics (CFD) predictions produced today focus on reduced or simplified versions of the real systems and are usually solved with a steady state assumption. This article shows how recent developments of CFD codes and parallel computer architectures can help overcoming this barrier. With this new environment, new scientific and technological challenges can be addressed provided that thousands of computing cores are efficiently used in parallel. Strategies of modern flow solvers are discussed with particular emphases on mesh-partitioning, load balancing and communication. These concepts are used in two CFD codes developed by CERFACS: a multi-block structured code dedicated to aircrafts and turbo-machinery as well as an unstructured code for gas turbine flow predictions. Leading edge computations obtained with these high-end massively parallel CFD codes are illustrated and discussed in the context of aircrafts, turbo-machinery and gas turbine applications. Finally, future developments of CFD and high-end computers are proposed to provide leading edge tools and end applications with strong industrial implications at the design stage of the next generation of aircraft and gas turbines.