  The rarefied flow and multi-scale flow are crucial for the aerodynamic design
of spacecraft, ultra-low orbital vehicles and plumes. By introducing a discrete
velocity space, the Boltzmann method, such as the discrete velocity method and
unified methods, can capture complex and non-equilibrium velocity distribution
functions (VDFs) and describe flow behaviors exactly. However, the extremely
steep slope and high concentration of the gas VDFs in a local particle velocity
space make it very difficult for the Boltzmann method with structured velocity
space to describe high speed flow. Therefore, the adaptive velocity space (AVS)
is required for the Boltzmann solvers to be practical in complex rarefied flow
and multi-scale flow. This paper makes two improvements to the AVS approach,
which is then incorporated into a general discrete velocity framework, such as
the unified gas-kinetic scheme. Firstly, a global velocity mesh is used to
prevent the interpolation of the VDFs at the physical interface during the
calculation of the microscopic fluxes, maintaining the program's high level of
parallelism. Secondly, rather than utilizing costly interpolation, the VDFs on
a new velocity space were reconstruction using the ``consanguinity"
relationship. In other words, a split child node's VDF is the same as its
parent's VDF, and a merged parent's VDF is the average of its children's VDFs.
Additionally, the discrete deviation of the equilibrium distribution functions
is employed to maintain the proposed method's conservation. Moreover, an
appropriate set of adaptive parameters is established to enhance the automation
of the proposed method. Finally, a number of numerical tests are carried out to
validate the proposed method.
