A new corner boundary condition for the discrete unified gas kinetic scheme

The implementation of the boundary condition at the corner points is very important. The discontinuities at the corner points propagate in the computational domain and have a great impact on the surrounding points and the global solution in the evolution process, resulting in the poor precision or the unphysical oscillatory behavior. However, it had been a largely under explored domain in the discrete unified gas kinetic scheme (DUGKS) methods. In the last few years, the DUGKS is proposed as a mesoscopic finite volume method with great development potential. In order to improve accuracy and efficiency, this paper proposes a new corner boundary condition for the DUGKS, which is deduced strictly in theory and available to satisfy conservation relations. The new corner boundary condition is validated by three numerical tests: the flow past a square cylinder (external flow), lid-driven cavity flow (internal flow) and flow past the AUV (nonright angle corner). The results show that the convergence efficiency and accuracy of the DUGKS are improved by the new corner boundary condition.