Abstract: In order to simulate gas flows with complex shapes or several bodies covering various regimes, coordinate space should be divided into dinky cells, and numerical method based on the complex mesh system should also be developed. In this paper, two-dimensional flows around complex objects are described by multi-block patched meshes, and then body-fitted mesh systems are given. Boltzmann-Rykov model equation involving rotational non-equilibrium effect is numerically computed based on this mesh system. Discrete velocity ordinate method is used to disperse velocity space, while finite-difference NND scheme for coordinate space. Transfer of distribution function on the interface, information and velocity information on the grid included, should be treated especially. Then flow characters from rarefied transition to continuum around complex bodies are obtained by numerical computing. Some examples show that macro-parameters glossily translate between different blocks in the whole mesh system. Results from GKUA are compared with those from reference and DSMC method. It is showed that the Gas-kinetic Unified Algorithm based on multi-block patched mesh is credible to numerically simulate complex flows in various regimes.