Performance evaluation of the general characteristics based off-lattice Boltzmann scheme and DUGKS for low speed continuum flows

Abstract

The general characteristics based off-lattice Boltzmann scheme (BKG) proposed by Bardow et al., [1] and the discrete unified gas kinetic scheme (DUGKS) [2] are two methods that successfully overcome the time step restriction by the collision time, which is commonly seen in many other kinetic schemes. Basically, the BKG scheme is a time splitting scheme, while the DUGKS is an un-split finite volume scheme. In this work, we first perform a theoretical analysis of the two schemes in the finite volume framework by comparing their numerical flux evaluations. It is found that the effects of collision term are considered in the reconstructions of the cell-interface distribution function in both schemes, which explains why they can overcome the time step restriction and can give accurate results even as the time step is much larger than the collision time. The difference between the two schemes lies in the treatment of the integral of the collision term, in which the Bardow's scheme uses the rectangular rule while the DUGKS uses the trapezoidal rule. The performance of the two schemes, i.e., accuracy, stability, and efficiency are then compared by simulating several two dimensional flows, including the unsteady Taylor-Green vortex flow, the steady lid-driven cavity flow, and the laminar boundary layer problem. It is observed that, the DUGKS can give more accurate results than the BKG scheme. Furthermore, the numerical stability of the BKG scheme decreases as the Courant-Friedrichs-Lewy (CFL) number approaches to 1, while the stability of DUGKS is not affected by the CFL number apparently as long as CFL < 1. It is also observed that the BKG scheme is about one time faster than the DUGKS scheme with the same computational mesh and time step.

Nonlinear oscillatory rarefied gas flow inside a rectangular cavity

“…In addition, DUGKS has second-order accuracy in both temporal and spatial discretizations. The capacity of DUGKS has been evaluated for gas flows by comparing with the lattice Boltzmann method [35][36][37][38], the spectral method [38,39], the DVM [40], and the DSMC [41,42]. It has also been successfully applied to study the phonon transport [43], turbulent flows [38,39,44], and thermally induced nonequilibrium flows [42].…”

Fluid flow around NACA 0012 airfoil at low-Reynolds numbers with hybrid lattice Boltzmann method

“…A different strategy to solve the lattice Boltzmann equation on nonuniform and unstructured meshes is based on Galerkin-type finite element methods and it has been introduced in [31,32,33,34]. Other approaches are the general characteristics based off-lattice Boltzmann scheme proposed by Bardow et al [35], the discrete unified gas kinetic scheme (DUGKS) [36] and the semi-lagrangian approach of Kramer et al [37]. In [38] a complete comparative study is performed to evaluate the performance of several explicit off-lattice Boltzmann methods.…”

Comparative study of the discrete velocity and the moment method for rarefied gas flows

“…the equations of reduced reference distribution functions eq eq gh ， can be found in [2,9]. Note that the dynamic viscosity  for the hard sphere (HS), and the variable hard-sphere model(VHS) is (8) where the generic symbol  is used to denote g or h.…”

“…There is a great need for efficient and accurate method for solving the Boltzmann equation. In the past two decades, various deterministic numerical methods have been developed to solve the Boltzmann equation, most of which are based on the DVM [2,3]. In the DVM, velocity phase has been reconstructed by a set of discrete velocity points, so that resulting equation can be solved numerically.…”