Development of discrete gas kinetic scheme for simulation of 3D viscous incompressible and compressible flows

作者：Yang, L. M.; Shu, C.^*; Wang, Y.; Sun, Y.

来源：Journal of Computational Physics, 2016, 319: 129-144.

DOI：10.1016/j.jcp.2016.05.018

• Discrete gas kinetic scheme
• 3D viscous flows
• Discrete velocity model
• Sphere function

The sphere function-based gas kinetic scheme (GKS), which was presented by Shu and his coworkers [ 23] for simulation of inviscid compressible flows, is extended to simulate 3D viscous incompressible and compressible flows in this work. Firstly, we use certain discrete points to represent the spherical surface in the phase velocity space. Then, integrals along the spherical surface for conservation forms of moments, which are needed to recover 3D Navier-Stokes equations, are approximated by integral quadrature. The basic requirement is that these conservation forms of moments can be exactly satisfied by weighted summation of distribution functions at discrete points. It was found that the integral quadrature by eight discrete points on the spherical surface, which forms the D3Q8 discrete velocity model, can exactly match the integral. In this way, the conservative variables and numerical fluxes can be computed by weighted summation of distribution functions at eight discrete points. That is, the application of complicated formulations resultant from integrals can be replaced by a simple solution process. Several numerical examples including laminar flat plate boundary layer, 3D lid-driven cavity flow, steady flow through a 90 degrees bending square duct, transonic flow around DPW-W1 wing and supersonic flow around NACA0012 airfoil are chosen to validate the proposed scheme. Numerical results demonstrate that the present scheme can provide reasonable numerical results for 3D viscous flows.

• 出版日期2016-8-15
• 单位南京航空航天大学