The high-order gas-kinetic scheme (HGKS) has been developed systematically for laminar flow simulation from nearly incompressible to hypersonic ones, which achieves a high-order accuracy in space and time as well as high efficiency and outstanding robustness. With the rapid increasing of computational power, it is fully legitimate to extend the advanced HGKS to the practical flow simulations. In this thesis, we mainly focus on the development of HGKS for the three-dimensional non-equilibrium flow modeling and simulations, namely the thermal non-equilibrium flows and the turbulent flows.

For non-equilibrium flow with multiple temperature, the Navier-Stokes equations lose accuracy partially due to the single temperature approximation. Targeting on accurate and effici...[ Read more ]

The high-order gas-kinetic scheme (HGKS) has been developed systematically for laminar flow simulation from nearly incompressible to hypersonic ones, which achieves a high-order accuracy in space and time as well as high efficiency and outstanding robustness. With the rapid increasing of computational power, it is fully legitimate to extend the advanced HGKS to the practical flow simulations. In this thesis, we mainly focus on the development of HGKS for the three-dimensional non-equilibrium flow modeling and simulations, namely the thermal non-equilibrium flows and the turbulent flows.

For non-equilibrium flow with multiple temperature, the Navier-Stokes equations lose accuracy partially due to the single temperature approximation. Targeting on accurate and efficient simulation of multi-temperature non-equilibrium flows, a three-dimensional multi-temperature HGKS is constructed, where a fourth-order Simpson interpolation rule is implemented for the newly emerged source term. Computational results confirm not only the high-order accuracy and quite robustness of this scheme, but also the significant improvement on computational efficiency, especially for the flow in the near continuum regime.

For the high-Reynolds number turbulent flows, an implicit HGKS with Lower-Upper Symmetric Gauss-Seidel technique is developed. Based on k ‒ ω SST model, a turbulent relaxation time is obtained and used in turbulent flow simulations. Comparisons among the numerical solutions from implicit HGKS, the explicit HGKS, the second-order implicit GKS, and experimental measurements have been conducted. It is concluded that the HGKS has high accuracy in space and time, especially for smooth flow, and obtains more accurate turbulent flow fields on coarse grids than the second-order GKS. In addition, significant acceleration on computational efficiency, as well as super robustness in simulating complex flow are confirmed from the implicit HGKS.

HGKS is implemented for large-scale direct numerical simulation of turbulent flows, and the parallel scalability, efficiency, accuracy and robustness of parallel implementation are validated. The performance of HGKS for the nearly incompressible turbulence is comparable with the high-order finite difference scheme, in terms of the resolution of flow structure and efficiency of computation. As a mesoscopic method, HGKS performs better than both lattice Boltzmann method and discrete unified gas-kinetic scheme, due to its higher order accuracy. Meanwhile, based on the kinetic formulation HGKS shows advantage in supersonic turbulent flow simulation with its high accuracy and outstanding robustness. In addition, for supersonic isotropic turbulence, the coarse-grained subgrid-scale turbulent kinetic energy K_sgs budget is fully analyzed for constructing one-equation subgrid-scale model in the compressible large eddy simulation.