Congshan Zhuo

Non-body-fitted Cartesian-mesh simulation of highly turbulent flows using multi-relaxation-time lattice Boltzmann method

This paper presents a lattice Boltzmann method (LBM) based study aimed at numerical simulation of highly turbulent and largely inclined flow around obstacles of curved geometry using non-body-fitted Cartesian meshes. The approach features (1) combining the interpolated bounce-back scheme with the LBM of multi-relaxation-time (MRT) type to enable the use of simple Cartesian mesh for the flow cases even with complex geometries; and (2) incorporating the Spalart-Allmaras (SA) turbulence model into LBM in order to represent the turbulent flow effect. The numerical experiments are performed corresponding to flows around an NACA0012 airfoil at Re=5x10^5 and around a flat plate at Re=2x10^4, respectively. The agreement between all simulation results obtained from this study and the data provided by other literature demonstrates the reliability of the enhanced LBM proposed in this paper for simulating, simply on Cartesian meshes, complex flows that may involve bodies of curved boundary, high Reynolds number, and large angle of attack.

Implementation of dual time-stepping strategy of the gas-kinetic scheme for unsteady flow simulations

In our study, the dual time-stepping strategy of the gas-kinetic scheme is constructed and used for the simulation of unsteady flows. In comparison to the previous implicit gas-kinetic scheme, both the inviscid and viscous flux Jacobian are considered in our work, and the linear system of the pseudo-steady-state is solved by applying generalized minimal residual algorithm. The accuracy is validated by several numerical cases, the incompressible flow around blunt bodies (stationary circular cylinder and square cylinder), and the transonic buffet on the NACA0012 airfoil under hybrid mesh. The numerical cases also demonstrate that the present method is applicable to approach the fluid flows from laminar to turbulent and from incompressible to compressible. Finally, the case of acoustic pressure pulse is carried out to evaluate the effects of enlarged time step, and the side effect of enlarged time step is explained. Compared with the explicit gas-kinetic scheme, the proposed scheme can greatly accelerate the computation and reduce the computational costs for unsteady flow simulations.

Filter-matrix lattice Boltzmann simulation of lid-driven deep-cavity flows, Part I - Steady flows

This paper seeks to make a systematic study over a series of lid-driven flow in various deep cavities using the filter-matrix lattice Boltzmann (FMLB) model. A concise description of the FMLB model is presented in this paper, and important numerical considerations for effective use of the FMLB model are also clearly elucidated. In particular, the selection of a free parameter employed to appropriately control the weight of the third-order terms in the FMLB solution vector is carefully examined, resulting in some general suggestions that may render the FMLB stability consistently secured for simulations of different cavity flow scenarios. Employing the FMLB and the lattice Bhatnagar-Gross-Krook (LBGK) methods for comparison purpose, the first series of test cases correspond to the lid-driven cavity flows with a low Reynolds number (Re=0.01) at a variety of aspect ratios; the simulation results demonstrate that the FMLB model is superior to the LBGK method in terms of numerical stability and, particularly, the FMLB result can reach quite good agreement with the benchmark solution even if the aspect ratio goes up to 15. Then, the FMLB model is used to compute the steady flows for deep cavities with aspect ratios ranging from 1.5 to 7 and elevated Reynolds numbers ranging from 100 to 5000; a number of features of steady flows, such as the locations, strengths, and sizes of the vortices, as well as the effects of Reynolds number and aspect ratio on the vortex structure, are all predicted by the FMLB model with an obviously improved accuracy when compared to some other available numerical results.

Filter-matrix lattice Boltzmann simulation of lid-driven deep-cavity flows, Part II - Flow bifurcation

Following the first part of this study, the filter-matrix lattice Boltzmann (FMLB) model is now applied to the investigation of the bifurcation behavior in the lid-driven deep-cavity flow. In this second part, the first Hopf bifurcations in the lid-driven cavity flow patterns with aspect ratios of 1-5 are examined in detail, revealing that the critical Reynolds number converges to a constant value with the increase of the cavity depth, and that the time-dependent vortex structures are periodic or quasi-periodic once this critical Reynolds number is exceeded. Through comparison against the relevant numerical results reported in the available literature, the present FMLB approach demonstrates its effectiveness and usefulness in studying the bifurcation phenomena arising in complex lid-driven deep-cavity flows.

An implicit gas-kinetic scheme for turbulent flow on unstructured hybrid mesh

This paper presents an implicit method for the discrete unified gas-kinetic scheme (DUGKS) to speed up the simulations of the steady flows in all flow regimes. The DUGKS is a multi-scale scheme finite volume method (FVM) for all flow regimes because of its ability in recovering the Navier-Stokes solution in the continuum regime and the free transport mechanism in rarefied flow, which couples particle transport and collision in the flux evaluation at cell interfaces. In this paper the predicted iterations are constructed to update the macroscopic variables and the gas distribution functions in discrete microscopic velocity space. The lower-upper symmetric GaussSeidel (LU-SGS) factorization is applied to solve the implicit equations. The fast convergence of implicit discrete unified gas-kinetic scheme (IDUGKS) can be achieved through the adoption of a numerical time step with large CFL number. Some numerical test cases, including the Couette flow, the lid-driven cavity flows under different Knudsen number and the hypersonic flow in transition flow regime around a circular cylinder, have been performed to validate this proposed IDUGKS. The computational efficiency of the IDUGKS to simulate the steady flows in all flow regimes can be improved by one or two orders of magnitude in comparison with the explicit DUGKS. PACS numbers: 47.45.Ab, 02.70.-c, 47.11.Df ∗ chungou@mail.nwpu.edu.cn † Corresponding author: zhongcw@nwpu.edu.cn ‡ zhuocs@nwpu.edu.cn 1 ar X iv :1 70 9. 01 81 9v 1 [ ph ys ic s. fl udy n] 6 S ep 2 01 7Abstract In this study, an implicit scheme for the gas-kinetic scheme (GKS) on the unstructured hybrid mesh is proposed. The Spalart–Allmaras (SA) one equation turbulence model is incorporated into the implicit gas-kinetic scheme (IGKS) to predict the effects of turbulence. The implicit macroscopic governing equations are constructed and solved by the matrix-free lower-upper symmetric-Gauss–Seidel (LU-SGS) method. To reduce the number of cells and computational cost, the hybrid mesh is applied. A modified non-manifold hybrid mesh data(NHMD) is used for both unstructured hybrid mesh and uniform grid. Numerical investigations are performed on different 2D laminar and turbulent flows. The convergence property and the computational efficiency of the present IGKS method are investigated. Much better performance is obtained compared with the standard explicit gas-kinetic scheme. Also, our numerical results are found to be in good agreement with experiment data and other numerical solutions, demonstrating the good applicability and high efficiency of the present IGKS for the simulations of laminar and turbulent flows.

A two-stage fourth-order gas-kinetic scheme on unstructured hybrid mesh

This paper presents an accurate and robust fourth order gas-kinetic scheme on two dimensional unstructured hybrid mesh for incompressible and compressible viscous flows. For generalized Riemann problem and Navier-Stokes solution, the gas-kinetic scheme (GKS) provides a time-accurate flux solver using a different way in the reconstruction at a cell interface in which two slopes for the equilibrium state are used. Different from the previous one-stage time-stepping method, the two-stage Lax-Wendroff type time stepping method is applied in this paper. Compared to standard four-stage fourth-order Runge-Kutta method, the two-stage fourth order time accurate method reduces the complexity of the adoption of time derivative of the flux function. To achieve fourth order accuracy, a finite volume method for GKS using cubic spline reconstruction is proposed on both structured grid and unstructured hybrid mesh. When dealing with flow discontinuities, the original spline scheme is replaced by the one blended with shock-capturing WENO scheme. Many one and two-dimensional test cases, including Couette flow, Shu-Osher problem, Woodward-Colella blast problem, two-dimensional Riemann problem, viscous shock tube flow, supersonic flow over a forward-facing step, and hypersonic flow over a circular cylinder, are carried out to demonstrate the performance of the proposed scheme.

A Unified Gas Kinetic Scheme for Transport and Collision Effects in Plasma

In this study, the Vlasov-Poisson equation with or without collision term for plasma is solved by the unified gas kinetic scheme (UGKS). The Vlasov equation is a differential equation describing time evolution of the distribution function of plasma consisting of charged particles with long-range interaction. The distribution function is discretized in discrete particle velocity space. After the Vlasov equation is integrated in finite volumes of physical space, the numerical flux across a cell interface and source term for particle acceleration are computed to update the distribution function at next time step. The flux is decided by Riemann problem and variation of distribution function in discrete particle velocity space is evaluated with central difference method. A electron-ion collision model is introduced in the Vlasov equation. This finite volume method for the UGKS couples the free transport and long-range interaction between particles. The electric field induced by charged particles is controlled by the Poissons equation. In this paper, the Poissons equation is solved using the Greens function for two dimensional plasma system subjected to the symmetry or periodic boundary conditions. Two numerical tests of the linear Landau damping and the Gaussian beam are carried out to validate the proposed method. The linear electron plasma wave damping is simulated based on electron-ion collision operator. Compared with previous methods, it is shown that the current method is able to obtain accurate results of the Vlasov-Poisson equation with a time step much larger than the particle collision time. Highly non-equilibrium and rarefied plasma flows, such as electron flows driven by electromagnetic field, can be simulated easily.

Physical Body Impact After High Altitude Bail-out

Abstract In most of the emergency circumstances, the aircrew leaves the aircraft under unsatisfied conditions, such as too high relative velocity to the ambient air or low partial oxygen pressure. The aircrew must pass through this area as quickly as possible before opening the parachute safely, viz., free-fall. Numerical simulations are conducted in this paper to explore the major characteristics of the aircrew free-fall process by using a commercial computational fluid dynamic (CFD) software, FLUENT. Coupled with the classical pressure-altitude and temperature-altitude relations, Navier-Stokes (N-S) equations for compressible flow are solved by using finite volume method. The body velocity and the attitude are predicted with six-degree of freedom (6DOF) module. The evolution of velocities, including horizontal, vertical components and angular velocity, is obtained. It is also analyzed further according to the particle kinetic theories. It is validated that the theories can predict the process qualitatively well with a modified drag effect, which mainly stems from the velocity pressure. An empirical modification factor is proposed according to the fitting results.