arXiv subjects

Congshan Zhuo

Publications and source records attributed to Congshan Zhuo.

26 records · Page 2Linked to original sources

arXiv2018

A simplified finite volume lattice Boltzmann method for simulations of fluid flows from laminar to turbulent regime, Part II: Extension towards turbulent flow simulation

In this paper, the finite volume lattice Boltzmann method (FVLBM) on unstructured grid presented in Part I of this paper is extended to simulate the turbulent flows. To model the turbulent effect, the $k-ω$ SST turbulence model is incorporated into the present FVLBM framework and also is solved by the finite volume method. Based on the eddy viscosity hypothesis, the eddy viscosity is computed from the solution of k-ωSST model, and the total viscosity is modified by adding this eddy viscosity to the laminar (kinematic) viscosity given in the Bhatnagar-Gross-Krook collision term. In order to enhance the computational efficiency, the three-stage second-order implicit-explicit (IMEX) Runge-Kutta method is used for temporal discretization and the time step can be larger one- or two-order of magnitude compared with explicit Euler forward scheme. Though the computational cost is increased, the finial computational efficiency is enhanced about one-order of magnitude and the good results also can be obtained at large time step through the test case of lid-driven cavity flow. Two turbulent flow cases are carried out to validate the present method, including flow over backward-facing step and flow around NACA0012 airfoil. Our numerical results are found to be in agreement with experimental data and numerical solutions, demonstrating applicability of the present FVLBM coupled with k-ωSST model to accurately predict the incompressible turbulent flows.

physics.comp-ph↗

arXiv2018

A phase-field model for large-density-ratio two-phase flows based on discrete unified gas-kinetic scheme

In this paper, a phase-field based model under the framework of discrete unified gas-kinetic scheme (DUGKS) for incompressible multiphase fluid flows is proposed. Two kinetic models are constructed to solve the conservative Allen-Cahn (A-C) equation that accounts for the interface behavior and the incompressible hydrodynamic equations that govern the flow field, respectively. With a truncated equilibrium distribution function as well as a temporal derivative added to the source term, the macroscopic governing equations can be exactly recovered from the kinetic models through the Chapmann-Enskog analysis. Calculation of source terms involving high-order derivatives existed in the quasi-incompressible model is simplified. A series of benchmark cases including four interface-capturing tests and four binary flow tests are carried out. Results compared to that of lattice Boltzmann method (LBM) have been obtained. A convergence rate of second-order can be guaranteed in the test of interface diagonal translation. The capability of present method in interface tracking that undergoes a severe deformation has been verified. Stationary bubble and spinodal decomposition problems, both with a density ratio as high as 1000, are conducted and reliable solutions have been provided. The layered Poiseuille flow with a large viscosity ratio is simulated and numerical results agree well with the analytical solutions. Variation of positions of the bubble front and spike tip during the evolution of Rayleigh-Taylor instability (RTI) has been predicted precisely. However, the detailed depiction of complicated interface patterns appeared in the evolution process is failed, which is mainly caused by the relatively large numerical dissipation of DUGKS compared to that of LBM. A high-order DUGKS is needed to overcome this problem.

physics.comp-ph↗

arXiv2018

A third order gas-kinetic scheme for unstructured grid

In our study, a compact third order gas-kinetic scheme is constructed for unstructured grid which is combined the compact least-square reconstruction (CLS) method. The CLS method can achieve arbitrary high order compact reconstruction using the stencil from the whole computational domain implicitly. A large sparse linear system resulted from the CLS reconstruction method is solved by applying the generalized minimal residual algorithm (GMRES), and the Reverse-Cuthill-McKee (RCM) algorithm and the incomplete lower-upper (ILU) factorization method are implemented to accelerate the convergence of the iterative method. Different from the traditional flux solver, the BGK based gas-kinetic scheme is in the nature of spatial and temporal accuracy. Applying the second order expansion to the distribution function, the third order flux solver can be obtained directly. The accuracy of present method is validated by several numerical cases such as the advection of density perturbation problem, Sod shock wave problem, Lax shock tube test case, Shu-Osher problem, shock-vortex interaction, and lid-driven cavity flow. The advantages of this high order gas-kinetic scheme are exhibited in some benchmarks including incompressible flow and supersonic compressible flow, inviscid flow and viscous flow.

physics.comp-ph↗

arXiv2018

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 Poisson's equation. In this paper, the Poisson's equation is solved using the Green's 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.

physics.comp-ph↗

arXiv2017

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.

physics.flu-dyn↗

arXiv2017

An Implicit Discrete Unified Gas-Kinetic Scheme for Simulations of Steady Flow in All Flow Regimes

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 Gauss-Seidel (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.

physics.flu-dyn↗

arXiv2017

An Implicit Gas-Kinetic Scheme for Turbulent Flow on Unstructured Hybrid Mesh

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 are 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.

physics.comp-ph↗

arXiv2016

Implementation of dual time stepping and GMRES of implicit gas-kinetic scheme for unsteady flow simulations

A dual time-stepping strategy of gas-kinetic scheme for the simulation of unsteady flows is introduced in this work. The dual time-stepping strategy is always used in the approaches of unsteady flows, and the ability of dual time-stepping to accelerate the computation with acceptable error tolerance is evident. In our paper, we adopt the techniques of dual time-stepping methods for implicit gas-kinetic scheme to simulate the unsteady flows, which is very popular for the numerical methods based on the Navier-Stokes equations. It is carried out by (a) solving the gas-kinetic scheme in finite volume method; (b) obtaining the inviscid flux Jacobian by Roe scheme; (c) involving the computation of viscous flux Jacobian which is not mentioned in the previous implicit gas-kinetic schemes; (d) approximating the linear system of pseudo steady state by generalized minimal residual algorithm (GMRES). The explicit gas-kinetic scheme has been proved to be an accurate approach for both the steady and unsteady flows, and the implicit gas-kinetic scheme is also be developed to accelerate the convergence of steady state. The dual time-stepping method proposed in our study is of great importance to the computations of unsteady flows. Several numerical cases are performed to evaluate the behavior of dual time stepping strategy of gas-kinetic scheme. The incompressible flow around blunt bodies (stationary circular cylinder and square cylinder) and the transonic buffet on the NACA0012 airfoil are simulated to demonstrate the overall performance of the proposed method which is applicable to the fluid flows from laminar to turbulent and from incompressible to compressible.

physics.flu-dyn↗