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Advection

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Pinghui Zhuang - One of the best experts on this subject based on the ideXlab platform.

Ian Turner - One of the best experts on this subject based on the ideXlab platform.

  • the fundamental solution and numerical solution of the riesz fractional Advection dispersion equation
    Ima Journal of Applied Mathematics, 2008
    Co-Authors: Shujun Shen, Ian Turner
    Abstract:

    In this paper, we consider a Riesz fractional Advection-dispersion equation (RFADE), which is derived from the kinetics of chaotic dynamics. The RFADE is obtained from the standard Advection-dispersion equation by replacing the first-order and second-order space derivatives by the Riesz fractional derivatives of order a e (0, 1) and fi e (1, 2], respectively. We derive the fundamental solution for the Riesz fractional Advection-dispersion equation with an initial condition (RFADE-IC). We investigate a discrete random walk model based on an explicit finite-difference approximation for the RFADE-IC and prove that the random walk model belongs to the domain of attraction of the corresponding stable distribution. We also present explicit and implicit difference approximations for the Riesz fractional Advection-dispersion equation with initial and boundary conditions (RFADE-IBC) in a finite domain. Stability and convergence of these numerical methods for the RFADE-IBC are discussed. Some numerical examples are given to show that the numerical results are in good agreement with our theoretical analysis.

  • time fractional Advection dispersion equation
    Journal of Applied Mathematics and Computing, 2003
    Co-Authors: Ian Turner, Pinghui Zhuang
    Abstract:

    A time fractional Advection-dispersion equation is obtained from the standard Advection-dispersion equation by replacing the firstorder derivative in time by a fractional derivative in time of order α(0<α<-1). Using variable transformation, Mellin and Laplace transforms, and properties of H-functions, we derive the complete solution of this time fractional Advection-dispersion equation.

  • Time fractional Advection-dispersion equation
    Journal of Applied Mathematics and Computing, 2003
    Co-Authors: Ian Turner, Pinghui Zhuang
    Abstract:

    A time fractional Advection-dispersion equation is obtained from the standard Advection-dispersion equation by replacing the firstorder derivative in time by a fractional derivative in time of order α(0

Huseyin Kocak - One of the best experts on this subject based on the ideXlab platform.

  • homotopy perturbation method for solving the space time fractional Advection dispersion equation
    Advances in Water Resources, 2009
    Co-Authors: Ahmet Yildirim, Huseyin Kocak
    Abstract:

    Abstract In this paper we present a reliable algorithm, the homotopy perturbation method, to construct numerical solutions of the space–time fractional Advection–dispersion equation in the form of a rapidly convergent series with easily computable components. Fractional Advection–dispersion equations are used in groundwater hydrology to model the transport of passive tracers carried by fluid flow in a porous medium. The fractional derivatives are described in the Caputo sense. Some examples are given. Numerical results show that the homotopy perturbation method is easy to implement and accurate when applied to space–time fractional Advection–dispersion equations.

Ahmet Yildirim - One of the best experts on this subject based on the ideXlab platform.

  • homotopy perturbation method for solving the space time fractional Advection dispersion equation
    Advances in Water Resources, 2009
    Co-Authors: Ahmet Yildirim, Huseyin Kocak
    Abstract:

    Abstract In this paper we present a reliable algorithm, the homotopy perturbation method, to construct numerical solutions of the space–time fractional Advection–dispersion equation in the form of a rapidly convergent series with easily computable components. Fractional Advection–dispersion equations are used in groundwater hydrology to model the transport of passive tracers carried by fluid flow in a porous medium. The fractional derivatives are described in the Caputo sense. Some examples are given. Numerical results show that the homotopy perturbation method is easy to implement and accurate when applied to space–time fractional Advection–dispersion equations.

Gianluigi Rozza - One of the best experts on this subject based on the ideXlab platform.

  • ENUMATH - Reduced Basis Approximation of Parametrized Advection-Diffusion PDEs with High Péclet Number
    Lecture Notes in Computational Science and Engineering, 2014
    Co-Authors: Paolo Pacciarini, Gianluigi Rozza
    Abstract:

    In this work we show some results about the reduced basis approximation of Advection dominated parametrized problems, i.e. Advection-diffusion problems with high Peclet number. These problems are of great importance in several engineering applications and it is well known that their numerical approximation can be affected by instability phenomena. In this work we compare two possible stabilization strategies in the framework of the reduced basis method, by showing numerical results obtained for a steady Advection-diffusion problem.

  • reduced basis approximation of parametrized Advection diffusion pdes with high peclet number
    Numerical Mathematics and Advanced Applications - ENUMATH 2013, 2014
    Co-Authors: Paolo Pacciarini, Gianluigi Rozza
    Abstract:

    In this work we show some results about the reduced basis approximation of Advection dominated parametrized problems, i.e. Advection-diffusion problems with high Peclet number. These problems are of great importance in several engineering applications and it is well known that their numerical approximation can be affected by instability phenomena. In this work we compare two possible stabilization strategies in the framework of the reduced basis method, by showing numerical results obtained for a steady Advection-diffusion problem.