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Rongzong Huang - One of the best experts on this subject based on the ideXlab platform.

  • lattice boltzmann model for the correct convection diffusion Equation with divergence free velocity field
    Physical Review E, 2015
    Co-Authors: Rongzong Huang
    Abstract:

    A lattice Boltzmann (LB) model for the Convection-Diffusion Equation (CDE) with divergence-free velocity field is proposed, and the Chapman-Enskog analysis shows that the CDE can be recovered correctly. In the present model, the convection term is treated as a source term in the lattice Boltzmann Equation (LBE) rather than being directly recovered by LBE; thus the CDE is intrinsically solved as a pure diffusion Equation with a corresponding source term. To avoid the adoption of a nonlocal finite-difference scheme for computing the convection term, a local scheme is developed based on the Chapman-Enskog analysis. Most importantly, by properly specifying the discrete source term in the moment space, the local scheme can reach the same order (ɛ^{2}) at which the CDE is recovered by a LB model. Numerical tests, including a one-dimensional periodic problem, diffusion of a Gaussian hill, diffusion of a rectangular pulse, and natural convection in a square cavity, are carried out to verify the present model. Numerical results are satisfactorily consistent with analytical solutions or previous numerical results, and show higher accuracy due to the correct recovery of CDE.

  • a modified multiple relaxation time lattice boltzmann model for convection diffusion Equation
    Journal of Computational Physics, 2014
    Co-Authors: Rongzong Huang
    Abstract:

    A modified lattice Boltzmann model with multiple relaxation times (MRT) for the Convection-Diffusion Equation (CDE) is proposed. By modifying the relaxation matrix, as well as choosing the corresponding equilibrium distribution function properly, the present model can recover the CDE with anisotropic diffusion coefficient with no deviation term even when the velocity vector varies generally with space or time through the Chapman-Enskog analysis. This model is firstly validated by simulating the diffusion of a Gaussian hill, which demonstrates it can handle the anisotropic diffusion problem correctly. Then it is adopted to calculate the longitudinal dispersion coefficient of the Taylor-Aris dispersion. Numerical results show that the present model can further reduce the numerical error under the condition of non-zero velocity vector, especially when the dimensionless relaxation time is relatively large.

Tianshou Zhao - One of the best experts on this subject based on the ideXlab platform.

  • nonequilibrium scheme for computing the flux of the convection diffusion Equation in the framework of the lattice boltzmann method
    Physical Review E, 2014
    Co-Authors: Zhenhua Chai, Tianshou Zhao
    Abstract:

    In this paper, we propose a local nonequilibrium scheme for computing the flux of the Convection-Diffusion Equation with a source term in the framework of the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). Both the Chapman-Enskog analysis and the numerical results show that, at the diffusive scaling, the present nonequilibrium scheme has a second-order convergence rate in space. A comparison between the nonequilibriumschemeandtheconventionalsecond-ordercentral-differenceschemeindicatesthat,althoughboth schemes have a second-order convergence rate in space, the present nonequilibrium scheme is more accurate than thecentral-differencescheme.Inaddition,thefluxcomputationrenderedbythepresentschemealsopreservesthe parallel computation feature of the LBM, making the scheme more efficient than conventional finite-difference schemes in the study of large-scale problems. Finally, a comparison between the single-relaxation-time model and the MRT model is also conducted, and the results show that the MRT model is more accurate than the single-relaxation-time model, both in solving the Convection-Diffusion Equation and in computing the flux.

  • lattice boltzmann model for the convection diffusion Equation
    Physical Review E, 2013
    Co-Authors: Zhenhua Chai, Tianshou Zhao
    Abstract:

    We propose a lattice Boltzmann (LB) model for the Convection-Diffusion Equation (CDE) and show that the CDE can be recovered correctly from the model by the Chapman-Enskog analysis. The most striking feature of the present LB model is that it enables the collision process to be implemented locally, making it possible to retain the advantage of the lattice Boltzmann method in the study of the heat and mass transfer in complex geometries. A local scheme for computing the heat and mass fluxes is then proposed to replace conventional nonlocal finite-difference schemes. We further validate the present model and the local scheme for computing the flux against analytical solutions to several classical problems, and we show that both the model for the CDE and the computational scheme for the flux have a second-order convergence rate in space. It is also demonstrated the present model is more accurate than existing LB models for the CDE.

Jun Zhang - One of the best experts on this subject based on the ideXlab platform.

  • a 15 point high order compact scheme with multigrid computation for solving 3d convection diffusion Equations
    International Journal of Computer Mathematics, 2015
    Co-Authors: Yin Wang, Su Yu, Jun Zhang
    Abstract:

    We propose a method with sixth-order accuracy to solve the three-dimensional (3D) convection diffusion Equation. We first use a 15-point fourth-order compact discretization scheme to obtain fourth-order solutions on both fine and coarse grids using the multigrid method. Then an iterative mesh refinement technique combined with Richardson extrapolation is used to approximate the sixth-order accurate solution on the fine grid. Numerical results are presented for a variety of test cases to demonstrate the efficiency and accuracy of the proposed method, compared with the standard fourth-order compact scheme.

  • fast and high accuracy multiscale multigrid method with multiple coarse grid updating strategy for the 3d convection diffusion Equation
    Computers & Mathematics With Applications, 2013
    Co-Authors: Yin Wang, Jun Zhang
    Abstract:

    An improved multiscale multigrid method with multiple coarse grid updating strategy for a three dimensional Convection-Diffusion Equation is presented. The novelty of the proposed method lies in a fine grid updating strategy arising from the idea of multiple coarse grid computation. The new fine grid updating strategy is able to replace the iterative refinement procedure in the existing multiscale multigrid method (Wang and Zhang, 2010) [16] to obtain high order solutions. Since the proposed method needs a fourth order compact scheme with unequal-meshsize grids, a 19 point fourth order compact difference scheme with unequal meshsize in different coordinate directions is also developed for the three dimensional Convection-Diffusion Equation. Numerical results are given to compare the computed accuracy and the computational efficiency of the multiscale multigrid method with the multiple coarse grid updating strategy against the multiscale multigrid method with the iterative refinement procedure.

  • truncation error and oscillation property of the combined compact difference scheme
    Applied Mathematics and Computation, 2005
    Co-Authors: Jun Zhang, Jennifer J Zhao
    Abstract:

    In this work, we study a sixth order combined compact difference scheme for a one dimensional convection diffusion Equation. We derive the truncation error representation and analyze its oscillation property. Numerical experiments are performed to illustrate and support our analysis.

  • a fourth order compact difference scheme on face centered cubic grids with multigrid method for solving 2d convection diffusion Equation
    Mathematics and Computers in Simulation, 2003
    Co-Authors: Ning Kang, Jun Zhang, Eric S. Carlson
    Abstract:

    We present a fourth-order compact finite difference scheme on the face centered cubic (FCC) grids for the numerical solution of the two-dimensional convection diffusion Equation. The seven-point formula is defined on a regular hexagon, where the strategy of directional derivative is employed to make the derivation procedure straightforward, efficient, and concise. A corresponding multigrid method is developed to solve the resulting sparse linear system. Numerical experiments are conducted to verify the fourth-order convergence rate of the derived discretization scheme and to show that the fourth-order compact difference scheme is computationally more efficient than the standard second-order central difference scheme.

  • convergence and performance of iterative methods for solving variable coefficient convection diffusion Equation with a fourth order compact difference scheme
    Computers & Mathematics With Applications, 2002
    Co-Authors: Samir Karaa, Jun Zhang
    Abstract:

    Abstract We conduct convergence analysis on some classical stationary iterative methods for solving the two-dimensional variable coefficient Convection-Diffusion Equation discretized by a fourth-order compact difference scheme. Several conditions are formulated under which the coefficient matrix is guaranteed to be an M-matrix. We further investigate the effect of different orderings of the grid points on the performance of some stationary iterative methods, multigrid method, and preconditioned GMRES. Three sets of numerical experiments are conducted to study the convergence behaviors of these iterative methods under the influence of the flow directions, the orderings of the grid points, and the magnitude of the convection coefficients.

Zhenhua Chai - One of the best experts on this subject based on the ideXlab platform.

  • Finite-difference lattice Boltzmann model for nonlinear Convection-Diffusion Equations
    Applied Mathematics and Computation, 2017
    Co-Authors: Huili Wang, Hong Liang, Zhenhua Chai
    Abstract:

    In this paper, a finite-difference lattice Boltzmann (LB) model for nonlinear isotropic and anisotropic Convection-Diffusion Equations is proposed. In this model, the equilibrium distribution function is delicately designed in order to recover the Convection-Diffusion Equation exactly. Different from the standard LB model, the temporal and spatial steps in this model are decoupled such that it is convenient to study Convection-Diffusion problem with the non-uniform grid. In addition, it also preserves the advantage of standard LB model that the complex-valued Convection-Diffusion Equation can be solved directly. The von Neumann stability analysis is conducted to discuss the stability region which can be used to determine the free parameters appeared in the model. To test the performance of the model, a series of numerical simulations of some classical problems, including the diffusion Equation, the nonlinear heat conduction Equation, the Sine-Gordon Equation, the Gaussian hill problem, the BurgersFisher Equation, and the nonlinear Schrdinger Equation, have also been carried out. The results show that the present model has a second-order convergence rate in space, and generally it is also more accurate than the standard LB model.

  • nonequilibrium scheme for computing the flux of the convection diffusion Equation in the framework of the lattice boltzmann method
    Physical Review E, 2014
    Co-Authors: Zhenhua Chai, Tianshou Zhao
    Abstract:

    In this paper, we propose a local nonequilibrium scheme for computing the flux of the Convection-Diffusion Equation with a source term in the framework of the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). Both the Chapman-Enskog analysis and the numerical results show that, at the diffusive scaling, the present nonequilibrium scheme has a second-order convergence rate in space. A comparison between the nonequilibriumschemeandtheconventionalsecond-ordercentral-differenceschemeindicatesthat,althoughboth schemes have a second-order convergence rate in space, the present nonequilibrium scheme is more accurate than thecentral-differencescheme.Inaddition,thefluxcomputationrenderedbythepresentschemealsopreservesthe parallel computation feature of the LBM, making the scheme more efficient than conventional finite-difference schemes in the study of large-scale problems. Finally, a comparison between the single-relaxation-time model and the MRT model is also conducted, and the results show that the MRT model is more accurate than the single-relaxation-time model, both in solving the Convection-Diffusion Equation and in computing the flux.

  • lattice boltzmann model for the convection diffusion Equation
    Physical Review E, 2013
    Co-Authors: Zhenhua Chai, Tianshou Zhao
    Abstract:

    We propose a lattice Boltzmann (LB) model for the Convection-Diffusion Equation (CDE) and show that the CDE can be recovered correctly from the model by the Chapman-Enskog analysis. The most striking feature of the present LB model is that it enables the collision process to be implemented locally, making it possible to retain the advantage of the lattice Boltzmann method in the study of the heat and mass transfer in complex geometries. A local scheme for computing the heat and mass fluxes is then proposed to replace conventional nonlocal finite-difference schemes. We further validate the present model and the local scheme for computing the flux against analytical solutions to several classical problems, and we show that both the model for the CDE and the computational scheme for the flux have a second-order convergence rate in space. It is also demonstrated the present model is more accurate than existing LB models for the CDE.

Yang Zhang - One of the best experts on this subject based on the ideXlab platform.

  • a finite difference method for fractional partial differential Equation
    Applied Mathematics and Computation, 2009
    Co-Authors: Yang Zhang
    Abstract:

    An implicit unconditional stable difference scheme is presented for a kind of linear space-time fractional Convection-Diffusion Equation. The Equation is obtained from the classical integer order Convection-Diffusion Equations with fractional order derivatives for both space and time. First-order consistency, unconditional stability, and first-order convergence of the method are proven using a novel shifted version of the classical Grunwald finite difference approximation for the fractional derivatives. A numerical example with known exact solution is also presented, and the behavior of the error is examined to verify the order of convergence.

  • finite difference approximations for space time fractional partial differential Equation
    Journal of Numerical Mathematics, 2009
    Co-Authors: Yang Zhang
    Abstract:

    An implicit difference scheme is presented for a space-time fractional Convection-Diffusion Equation. The Equation is obtained from the classical integer order Convection-Diffusion Equations with fractional order derivatives for both space and time. First-order consistency, unconditional stability, and first-order convergence of the method are proven using a novel shifted version of the classical Grunwald finite difference approximation for the fractional derivatives. A numerical example with known exact solution is also presented, and the behavior of the error is examined to verify the order of convergence.