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In this paper, a variant of the improved discrete velocity method (VIDVM) is proposed for flows in the whole Knudsen number regimes. This method retains the advantage of the improved discrete velocity method (IDVM), which calculates numerical fluxes through a self-adaptive strategy by combining the microscopic reconstruction and the macroscopic reconstruction. Like the IDVM, the microscopic reconstruction for VIDVM is also based on the collisionless Boltzmann solver. However, different from IDVM, the macroscopic reconstruction for VIDVM is established on the Euler solver instead of the Navier–Stokes solver. Considering that the Euler solver merely computes the inviscid fluxes while the Navier–Stokes solver additionally calculates the viscous fluxes, the present method could be more efficient than IDVM. To validate the accuracy and efficiency of the present scheme, some benchmark cases from the continuum regime to the free molecular regime are conducted. Results reveal that the present scheme can predict the flow as well as IDVM, but the present solver is more efficient than IDVM. [ABSTRACT FROM AUTHOR]

The Grad's 13 distribution function was derived through a third-order Hermite polynomial expansion in terms of peculiar velocity. Recently, it has been adopted to construct a gas kinetic flux solver called G13-GKFS for simulation of flows from the continuum regime to the rarefied regime. However, this Grad's distribution function only considers the contracted polynomials that strictly satisfy orthogonality. In other words, the third-order terms of C i C 1 2 , C i C 2 2 , and C i C 3 2 share the same coefficients ( γ i ). However, the results from the discrete velocity method reveal that those coefficients could be different, especially in the rarefied regime. This may affect the accuracy of numerical results in the rarefied region. In order to consider different coefficients of the third-order terms, we propose a complete third-order polynomial expansion to approximate the distribution function in this work. To show the capability of current distribution function, a new GKFS is developed for flows from the continuum regime to the rarefied regime. Some benchmark cases are solved to demonstrate that the new GKFS outperforms the G13-GKFS in the rarefied regime. [ABSTRACT FROM AUTHOR]

The oblique drop impact on the thin film is numerically investigated in this paper with special attention paid to its splashing dynamics at moderate impingement angles (45° ≤ α ≤ 75°). A three-dimensional multiphase lattice Boltzmann flux solver associated with the diffuse interface method is adopted after being validated against reference data. Efforts are made to recover the complex flow features in the oblique drop impact on the thin film at various impingement angles, film thicknesses (δ), Ohnesorge numbers (Oh), and Weber numbers (We). We found that the later stage of radial propagation of the jet base and the free rim is dominated by inertia and can be well correlated with dimensionless time τ through the square-root law. The elevation of the free rim exhibits a linear relationship with time and varies with Oh and We, indicating its connection to the splashing of minor droplets, which is also an outcome of inertia, viscosity, and surface tension. Moreover, the onset of droplet splashing is generally insensitive to δ. Based on that, a correlation between the splashing limit and the impingement angle is established and shows good agreement with numerical results at moderate impingement angles. [ABSTRACT FROM AUTHOR]

An immersed boundary–simplified lattice Boltzmann method (IB-STLBM) is proposed in this paper for the simulation of incompressible thermal flows with immersed objects. The fractional step technique is adopted to resolve the problem in two successive steps. In the predictor step, the simplified thermal lattice Boltzmann method (STLBM) is utilized to resolve the intermediate flow variables without considering the immersed objects. The STLBM is advantageous over the conventional thermal lattice Boltzmann method (TLBM) in memory cost, boundary treatment, and numerical stability. In the corrector step, the boundary condition-enforced immersed boundary method (IBM) is used to give correction values of velocity and temperature for accurate interpretation of the Dirichlet boundary conditions on the surface of the immersed objects. Based on the present IBM, some novel strategies can be applied in the evaluation of hydrodynamic forces or thermal parameters of the immersed objects. Five numerical examples are presented for comprehensive validation of the accuracy and robustness of IB-STLBM in various two- and three-dimensional thermal flow problems. [ABSTRACT FROM AUTHOR]

In this work, we propose an improved discrete gas-kinetic scheme (DGKS) for viscous incompressible and compressible flows based on the modified circular function. The improved scheme restores the flaw of the previous DGKS and recovers the correct macroscopic energy equation. Modifications are first made on the previous circular function by relocating some portion of the particles in the phase velocity space from the circle to the circular center. By adjusting the portion of particles at the circular center, the true diffusive flux for the energy equation can be recovered, and thus, the correct macroscopic energy equation is obtained. Based on the modified circular function, a D2Q5 discrete velocity model is developed, which enhances the computational efficiency. This discrete velocity model is then incorporated into the finite volume framework for the reconstruction of numerical fluxes on the cell interface. Numerical tests on incompressible and compressible flows are performed for comprehensive validation of the proposed solver. Improved accuracy is observed in the test examples, and the computational results show good agreement with the reference data. [ABSTRACT FROM AUTHOR]