Optimized discrete unified gas kinetic scheme for continuum and rarefied flows

In this paper, an optimized discrete unified gas kinetic scheme (DUGKS) is presented for both continuum and rarefied flow. The present scheme can be considered as a new version of the DUGKS. At first we follow the original DUGKS to obtain the evolution equation by finite volume method. Then we propose a new method to evaluate the flux. Different from the original DUGKS, the flux is evaluated by the distribution function at the node instead of the interface center. This makes the present scheme easier to implement, and more efficient than the original DUGKS. To validate the present scheme, several numerical tests are performed, including the doubly periodic shear layers, the canonical two-dimension and three-dimension Taylor-Green vortex flows, as well as the pressure-driven couette flow and micro-couette flow. Numerical results demonstrate that, the present scheme preserves almost the same accuracy as compared with the original DUGKS, while it exhibits a lower numerical dissipation, and the computational efficiency as well as numerical stability can be significantly improved.