A regularized discrete unified gas-kinetic scheme for incompressible viscous flows

In computational fluid dynamics, the Gauss-Hermite-quadrature-based mesoscopic methods, including the lattice Boltzmann method (LBM), the discrete unified gas kinetic scheme (DUGKS), have attracted much attention in the past decades. Similar to the LBM, DUGKS, as a second-order finite volume method, has the flexibility of using non-uniform and non-structured grids and maintains the asymptotic persevering property when simulating continuum flows. However, these approaches may encounter numerical instability when the flow Reynolds number and Mach number exceed certain limits. To enhance the numerical stability, regularization has been introduced to remove spurious moments, by projecting the distribution function onto the Hilbert space with a specific Gauss-Hermite quadrature accuracy. In this poster, we apply such regularization to the DUGKS approach, to examine its effects on the numerical stability and physical accuracy. Preliminary numerical results for three-dimensional decaying homogeneous isotropic turbulence illustrate that the regularization significantly enhances the numerical stability for athermal flows without affecting the accuracy of physical results.