Multiscale lattice Boltzmann approach to modeling gas flows

Abstract

For multiscale gas flows, kinetic-continuum hybrid method is usually used to balance the computational accuracy and efficiency. However, the kinetic-continuum coupling is not straightforward since the coupled methods are based on different theoretical frameworks. In particular, it is not easy to recover the non-equilibrium information required by the kinetic method which is lost by the continuum model at the coupling interface. Therefore, we present a multiscale lattice Boltzmann (LB) method which deploys high-order LB models in highly rarefied flow regions and low-order ones in less rarefied regions. Since this multiscale approach is based on the same theoretical framework, the coupling precess becomes simple. The non-equilibrium information will not be lost at the interface as low-order LB models can also retain this information. The simulation results confirm that the present method can achieve model accuracy with reduced computational cost.

Gaussian Lattice Boltzmann method and its applications to rarefied flows

“…The discrepancy between the model solution and the tabulated data is approximately 10% for the Knudsen numbers in the part of the ballistic regime 1 ≤ Kn ≤ 3.33. Similar result can be obtained for an even-velocity high-order D2Q4624 off-lattice LB model with one relaxation time [13]. In the present case the fully symmetric 2D Gaussian LB model for N = 13 in the 2N + 2 hierarchy has 28 * 28 = 784 velocities (G-D2Q784).…”

“…4). The positive effect of zero velocity removal is thoroughly explained in [13,16]. Zero velocity usually has the lattice weight significantly greater than the weights of the other velocities, on the other hand zero-velocity weight does not influence half-moments (or half-fluxes) which enter the kinetic boundary conditions.…”

“…The latter expression leads to the same result. The fourth moment can be obtained from the moment generating function or by computing Y 4 = ( N j X j ) 4 , after some lengthy algebra one obtains the following result For 2N + 2 hierarchy the moment generating function was not obtained, the third moment is then computed in a straightforward way finally remembering that the temperature for 2N + 2 hierarchy is given by the relation (13) i.e. equals θ 0 + c 2 4 one can conclude that the error is again u 2 /N 3 in comparison with the local Maxwell third moment.…”

Discrete Boltzmann modeling of Rayleigh-Taylor instability in two-component compressible flows

“…To investigate those complex nonequilibrium manifestations, a rigorous approach is to employ the Boltzmann equation [13][14][15][16][17][18][19][20] which describes the evolution of nonequilibrium statistical physical systems. However, solving the Boltzmann equation directly is computationally prohibitive.…”

Steady-State Anderson Accelerated Coupling of Lattice Boltzmann and Navier–Stokes Solvers

“…Besides, capturing different flow physics by using an efficient LBNS coupling may be enabled. For example, the mesoscopic nature of LB allows to access finite Knudsen flows for regimes up to Kn ∼ O(1) [22,23], potentially using higher-order LB velocity space discretizations. Flows in micro-devices such as microfluidic networks may thus be simulated using a NS solver in wider bulk regions and a LB solver in narrow regions.…”