A simplified circular function–based gas kinetic scheme for simulation of incompressible flows

Abstract

Summary In this paper, the circular function–based gas kinetic scheme (GKS), which is often applied for simulation of compressible flows, is simplified to improve computational efficiency for simulation of incompressible flows. In the original circular function–based GKS, the integral domain along the circle for computing conservative variables and numerical fluxes is usually not symmetric at the cell interface. This leads to relatively complicated formulations for computing the numerical flux at the cell interface. As shown in this work, for incompressible flows, the circle at the cell interface can be approximately considered to be symmetric. As a consequence, the simple expressions for calculation of conservative variables and numerical fluxes at the cell interface can be obtained, and computational efficiency is greatly improved. In the meanwhile, like the original circular function–based GKS, the discontinuity of conservative variables and their derivatives at the cell interface is still kept in the present scheme to keep good numerical stability at high Reynolds numbers. Several numerical examples, including decaying vortex flow, lid‐driven cavity flow, and flow past a stationary and rotating circular cylinder, are tested to validate the accuracy, efficiency, and stability of the present scheme.

A mesh‐free radial basis function–based semi‐Lagrangian lattice Boltzmann method for incompressible flows

“…[29][30][31][32][33][34][35] The Reynolds number is defined as Re = u 0 L/ , where u 0 is the lid velocity and L is the length of cavity. [29][30][31][32][33][34][35] The Reynolds number is defined as Re = u 0 L/ , where u 0 is the lid velocity and L is the length of cavity.…”

“…In this section, the lid-driven cavity flows at Re = 100, 1000, 3200, and 5000 are simulated. Moreover, other results in the literature [29][30][31][32][33][34][35] are also listed in Table 2 for comparison. The number of support points for the local RBF interpolation is np = 16 in the cases of Re = 100 and 1000, and np = 36 in the cases of Re = 3200 and 5000.…”

“…The bounce-back boundary condition is applied at four boundaries. [29][30][31][32][33][34][35] (A) Re=100 (B) Re=1000 Firstly, locations of primary vortex centers at different Reynolds numbers are measured and listed in Table 2.…”

Numerical investigation on performance of three solution reconstructions at cell interface in DVM simulation of flows in all Knudsen number regimes

“…To compare the solution accuracy and computational efficiency of different methods in the two‐dimensional case, the lid‐driven cavity flow with various Knudsen and Reynolds numbers is simulated. This problem has been widely studied both in the rarefied flow regime and in the continuum flow regime . The computational domain of this test example is a square cavity with the edge length of L .…”

“…This problem has been widely studied both in the rarefied flow regime 13,27,33,34,[47][48][49] and in the continuum flow regime. [50][51][52][53][54] The computational domain of this test example is a square cavity with the edge length of L. At the top wall, the temperature and velocity are fixed at T 0 = 273 K and u 0 = 0.15 √ 2 0 , respectively. Remaining three walls are stationary and in constant temperature of T 0 .…”