Vectorial discrete unified gas kinetic scheme for continuum compressible flows

Abstract

A vectorial discrete unified gas kinetic scheme (V-DUGKS) is proposed for continuum compressible flows. In the vectorial kinetic framework, mass, momentum, and total energy are represented by coupled distribution functions with separate relaxation processes for momentum and energy transport, enabling an adjustable Prandtl number. All equilibrium distributions are truncated at the second-order Hermite level. Since only second-order velocity moments are required to recover the compressible Navier-Stokes equations, fourth-order Gauss-Hermite quadrature is sufficient for exact moment evaluation. Eliminating third-order Hermite terms allows compact discrete velocity sets to be used uniformly for all distribution functions, reducing sensitivity to the numerical reference temperature and improving stability and efficiency over the scalar DUGKS. The scheme employs a finite-volume formulation with characteristic-based flux evaluation and trapezoidal collision integration. Numerical tests, including shock-tube, Shu-Osher, two-dimensional Riemann, and three-dimensional Taylor-Green vortex problems, demonstrate its accuracy and robustness. For the three-dimensional Taylor-Green vortex, V-DUGKS achieves a speed-up of about 2.2-2.9 under the same CFL constraint due to a larger allowable time step and simplified equilibrium formulation. These results show that V-DUGKS provides a robust and efficient kinetic framework for continuum compressible flow simulations.