Abstract: Conventional Discrete Velocity Method (DVM) only resolves the kinetic equation (i.e., Boltzmann-BGK equation) in each time step for fluid flow problem simulation in all flow regimes. Different from the conventional method, the Improved Discrete Velocity Method (IDVM) solves both the kinetic equation and the corresponding macroscopic governing equations so that the collisional effect at the cell interface can be involved in the calculation of numerical flux and the fully implicit discretization of the kinetic equation realized by the predicted results of macroscopic governing equations. These two improvements can effectively overcome the defects of low efficiency and poor accuracy of the conventional DVM in the continuum flow regime. To further reduce the number of discrete points in the velocity space and avoid the Runge phenomenon for numerical quadrature, the unstructured mesh combined with the rectangle rule is utilized to discretize the velocity space, and the conservative correction introduced to enforce the compatibility condition. Numerical results show that these strategies can significantly reduce the computational cost and memory consumption of the present method.

Key words: discrete velocity method, fully implicit scheme, unstructured mesh, conservative correction, computational efficiency