NRxx Simulation of Microflows with Finite Volume Method

Although three-dimensional space NRxx(3D-NRxx) method[1] has some useful numerical properties and is valid for big Knudson number, its high computational cost results limited applications. Based on the idea of limitting three-dimensional space Boltzmann equation on two-dimensional space[2], we apply 3D-NRxx method on two-dimensional space, to get two-dimensional NRxx(2D-NRxx) method. In order to make 2D-NRxxmethod more efficient, we concentrate on the regularization of moment system. Both BGK model and Shakhov model are studied. We also introduce Maxwellian boundary condition and create a frame to deal with it. Numerically, convection part and collision part are splitted by splitting method. While collision part can be solved exactly without changing macroscopic quantity, HLL scheme is introduced to calculate the convection part. To optimize 2D-NRxx, we construct a 2nd order scheme by including the 2nd order splitting scheme, the RKC schemes to relieve the time step length, and the 2nd order HLL flux with linear reconstruction. Finally, we have validated the 2D-NRxxmethod, the 2nd order scheme, and the boundary condition by calculating some classic numerical examples.