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Register a new userKinetic multiscale scheme based on the discrete-velocity and lattice-Boltzmann methods
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A novel hybrid computational method based on the discrete-velocity (DV) approximation, including the lattice-Boltzmann (LB) technique, is proposed. Numerical schemes for the kinetic equations are used in regions of rarefied flows, and LB schemes are employed in continuum flow zones. The schemes are written under the finite-volume (FV) formulation to achieve the flexibility of local mesh refinement. The truncated Hermite polynomial expansion is used for matching of DV and LB solutions. Special attention is paid to preserving conservation properties in the coupling algorithm. The test results obtained for the Couette flow of a rarefied gas are in excellent agreement with the benchmark solutions, mostly thanks to mesh refinement (both in the physical and velocity spaces) in the Knudsen layer.
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In this paper, authors focus effort on improving the conventional discrete velocity method (DVM) into a multiscale scheme in finite volume framework for gas flow in all flow regimes. Unlike the typical multiscale kinetic methods unified gas-kinetic scheme (UGKS) and discrete unified gas-kinetic scheme (DUGKS), which concentrate on the evolution of the distribution function at the cell interface, in the present scheme the flux for macroscopic variables is split into the equilibrium part and the nonequilibrium part, and the nonequilibrium flux is calculated by integrating the discrete distribution function at the cell center, which overcomes the excess numerical dissipation of the conventional DVM in the continuum flow regime. Afterwards, the macroscopic variables are finally updated by simply integrating the discrete distribution function at the cell center, or by a blend of the increments based on the macroscopic and the microscopic systems, and the multiscale property is achieved. Several test cases, involving unsteady, steady, high speed, low speed gas flows in all flow regimes, have been performed, demonstrating the good performance of the multiscale DVM from free molecule to continuum Navier-Stokes solutions and the multiscale property of the scheme is proved.
This paper proposes an improved lattice Boltzmann scheme for incompressible axisymmetric flows. The scheme has the following features. First, it is still within the framework of the standard lattice Boltzmann method using the single-particle density distribution function and consistent with the philosophy of the lattice Boltzmann method. Second, the source term of the scheme is simple and contains no velocity gradient terms. Owing to this feature, the scheme is easy to implement. In addition, the singularity problem at the axis can be appropriately handled without affecting an important advantage of the lattice Boltzmann method: the easy treatment of boundary conditions. The scheme is tested by simulating Hagen-Poiseuille flow, three-dimensional Womersley flow, Wheeler benchmark problem in crystal growth, and lid-driven rotational flow in cylindrical cavities. It is found that the numerical results agree well with the analytical solutions and/or the results reported in previous studies.
In this paper, we develop a discrete unified gas kinetic scheme (DUGKS) for general nonlinear convection-diffusion equation (NCDE), and show that the NCDE can be recovered correctly from the present model through the Chapman-Enskog analysis. We then test the present DUGKS through some classic convection-diffusion equations, and find that the numerical results are in good agreement with analytical solutions and the DUGKS model has a second-order convergence rate. Finally, as a finite-volume method, DUGKS can also adopt the non-uniform mesh. Besides, we performed some comparisons among the DUGKS, finite-volume lattice Boltzmann model (FV-LBM), single-relaxation-time lattice Boltzmann model (SLBM) and multiple-relaxation-time lattice Boltzmann model (MRT-LBM). The results show that the DUGKS model is more accurate than FV-LBM, more stable than SLBM, and almost has the same accuracy as the MRT-LBM. Besides, the using of non-uniform mesh may make DUGKS model more flexible.
The discrete unified gas kinetic scheme (DUGKS) is a new finite volume (FV) scheme for continuum and rarefied flows which combines the benefits of both Lattice Boltzmann Method (LBM) and unified gas kinetic scheme (UGKS). By reconstruction of gas distribution function using particle velocity characteristic line, flux contains more detailed information of fluid flow and more concrete physical nature. In this work, a simplified DUGKS is proposed with reconstruction stage on a whole time step instead of half time step in original DUGKS. Using temporal/spatial integral Boltzmann Bhatnagar-Gross-Krook (BGK) equation, the transformed distribution function with inclusion of collision effect is constructed. The macro and mesoscopic fluxes of the cell on next time step is predicted by reconstruction of transformed distribution function at interfaces along particle velocity characteristic lines. According to the conservation law, the macroscopic variables of the cell on next time step can be updated through its macroscopic flux. Equilibrium distribution function on next time step can also be updated. Gas distribution function is updated by FV scheme through its predicted mesoscopic flux in a time step. Compared with the original DUGKS, the computational process of the proposed method is more concise because of the omission of half time step flux calculation. Numerical time step is only limited by the Courant-Friedrichs-Lewy (CFL) condition and relatively good stability has been preserved. Several test cases, including the Couette flow, lid-driven cavity flow, laminar flows over a flat plate, a circular cylinder, and an airfoil, as well as micro cavity flow cases are conducted to validate present scheme. The numerical simulation results agree well with the references results.
We describe how regularization of lattice Boltzmann methods can be achieved by modifying dissipation. Classes of techniques used to try to improve regularization of LBMs include flux limiters, enforcing the exact correct production of entropy and manipulating non-hydrodynamic modes of the system in relaxation. Each of these techniques corresponds to an additional modification of dissipation compared with the standard LBGK model. Using some standard 1D and 2D benchmarks including the shock tube and lid driven cavity, we explore the effectiveness of these classes of methods.
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