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Zhen F. Tian - One of the best experts on this subject based on the ideXlab platform.

  • a high order compact scheme for the pure streamfunction vector potential formulation of the 3d steady incompressible navier stokes equations
    Journal of Computational Physics, 2019
    Co-Authors: Zhen F. Tian
    Abstract:

    Abstract In this paper, a high-order compact finite difference algorithm is proposed for the pure streamfunction (vector potential) formulation of the three dimensional steady incompressible Navier–Stokes equations, in which the grid values of the streamfunction (vector potential), its first-order and second-order derivatives are carried as the unknown variables. The numerical boundary schemes are also established for a general set of flow problems with no normal speed on the boundaries. Numerical examples, including a test problem with an analytical solution and three types of lid-driven cubic cavity flow problems, are solved numerically by the newly proposed scheme. The results obtained prove that the present numerical method has the ability to solve the three dimensional incompressible flow with high accuracy.

  • A high-order compact scheme for the pure streamfunction (vector potential) formulation of the 3D steady incompressible Navier–Stokes equations
    Journal of Computational Physics, 2019
    Co-Authors: Zhen F. Tian
    Abstract:

    Abstract In this paper, a high-order compact finite difference algorithm is proposed for the pure streamfunction (vector potential) formulation of the three dimensional steady incompressible Navier–Stokes equations, in which the grid values of the streamfunction (vector potential), its first-order and second-order derivatives are carried as the unknown variables. The numerical boundary schemes are also established for a general set of flow problems with no normal speed on the boundaries. Numerical examples, including a test problem with an analytical solution and three types of lid-driven cubic cavity flow problems, are solved numerically by the newly proposed scheme. The results obtained prove that the present numerical method has the ability to solve the three dimensional incompressible flow with high accuracy.

  • A compact streamfunction-velocity scheme for the 2-D unsteady incompressible Navier-Stokes equations in arbitrary curvilinear coordinates
    Journal of Hydrodynamics, 2018
    Co-Authors: Jian-xin Qiu, Bo Peng, Zhen F. Tian
    Abstract:

    A streamfunction-velocity formulation-based compact difference method is suggested for solving the unsteady incompressible Navier-Stokes equations in the arbitrary curvilinear coordinates, in which the streamfunction and its first derivatives as the unknown variables are utilized. Numerical examples, involving the boundary layer problem, a constricted channel flow, driven polar cavity flow and trapezoidal cavity flow problem, are solved by the present method. Numerical results demonstrate the accuracy of the proposed scheme and exhibit the numerical capability to simulate the flow problems on geometries beyond rectangular. For driven polar cavity flow problem, the results show that the flow for Re = 5 000 is not steady but time-periodic, and the critical Reynold number (Rec) for the occurrence of a Hopf bifurcation is given.

  • an upwind compact difference scheme for solving the streamfunction velocity formulation of the unsteady incompressible navier stokes equation
    Computers & Mathematics With Applications, 2018
    Co-Authors: Zhen F. Tian
    Abstract:

    Abstract In this paper, an upwind compact difference method with second-order accuracy both in space and time is proposed for the streamfunction–velocity formulation of the unsteady incompressible Navier–Stokes equations. The first derivatives of streamfunction (velocities) are discretized by two type compact schemes, viz. the third-order upwind compact schemes suggested with the characteristic of low dispersion error are used for the advection terms and the fourth-order symmetric compact scheme is employed for the biharmonic term. As a result, a five point constant coefficient second-order compact scheme is established, in which the computational stencils for streamfunction only require grid values at five points at both ( n ) th and ( n + 1 ) th time levels. The new scheme can suppress non-physical oscillations. Moreover, the unconditional stability of the scheme for the linear model is proved by means of the discrete von Neumann analysis. Four numerical experiments involving a test problem with the analytic solution, doubly periodic double shear layer flow problem, lid driven square cavity flow problem and two-sided non-facing lid driven square cavity flow problem are solved numerically to demonstrate the accuracy and efficiency of the newly proposed scheme. The present scheme not only shows the good numerical performance for the problems with sharp gradients, but also proves more effective than the existing second-order compact scheme of the streamfunction–velocity formulation in the aspect of computational cost.

  • An upwind compact difference scheme for solving the streamfunction–velocity formulation of the unsteady incompressible Navier–Stokes equation
    Computers & Mathematics with Applications, 2018
    Co-Authors: Zhen F. Tian
    Abstract:

    Abstract In this paper, an upwind compact difference method with second-order accuracy both in space and time is proposed for the streamfunction–velocity formulation of the unsteady incompressible Navier–Stokes equations. The first derivatives of streamfunction (velocities) are discretized by two type compact schemes, viz. the third-order upwind compact schemes suggested with the characteristic of low dispersion error are used for the advection terms and the fourth-order symmetric compact scheme is employed for the biharmonic term. As a result, a five point constant coefficient second-order compact scheme is established, in which the computational stencils for streamfunction only require grid values at five points at both ( n ) th and ( n + 1 ) th time levels. The new scheme can suppress non-physical oscillations. Moreover, the unconditional stability of the scheme for the linear model is proved by means of the discrete von Neumann analysis. Four numerical experiments involving a test problem with the analytic solution, doubly periodic double shear layer flow problem, lid driven square cavity flow problem and two-sided non-facing lid driven square cavity flow problem are solved numerically to demonstrate the accuracy and efficiency of the newly proposed scheme. The present scheme not only shows the good numerical performance for the problems with sharp gradients, but also proves more effective than the existing second-order compact scheme of the streamfunction–velocity formulation in the aspect of computational cost.

Yves Plancherel - One of the best experts on this subject based on the ideXlab platform.

  • On the relationships between features of the depth–latitude meridional overturning Streamfunctions across global coupled climate models
    Climate Dynamics, 2014
    Co-Authors: Yves Plancherel
    Abstract:

    A comparative analysis of the state and response of the latitude–depth meridional overturning Streamfunctions in the Climate Model Inter-comparison Project 3 (CMIP3) model set is presented. Simulated overturning strengths of the North Atlantic cell tend to converge towards observational estimates. The models whose simulations of the North Atlantic cell are closest to observational estimates indicate a 29.5 ± 13 % decrease in the maximum intensity of that cell by 2,100. In contrast, agreement with regard to the state and the response to anthropogenic radiative forcing of the global Southern Ocean abyssal cell is poor among the models. A weak relationship between the mean state and the response of the abyssal cell can be used to constrain the reduction of the Southern abyssal cell by 2,100 to 29.3 ± 20.7 %, in rough agreement with the decrease predicted in the Northern cell. The biases across the CMIP3 models in the Northern deep cell and Southern abyssal cell cannot be related dynamically by a buoyancy-based seesaw-like argument. The absence or presence of characteristic relationships between the state and evolution of different features of the overturning streamfunction indicate that the main reasons for across-model spread are how each model deals with subgrid-scale processes and viscosity. This highlights the fact that subgrid-scale parameterizations and resolution improvements should be a priority of model development. These factors are able to explain qualitatively the inter-model differences between the Northern overturning cells of the different models. Across-model differences in the winds over the Southern Ocean are responsible for much of the disparity in the overturning circulation cells of the Southern Ocean.

  • on the relationships between features of the depth latitude meridional overturning Streamfunctions across global coupled climate models
    Climate Dynamics, 2014
    Co-Authors: Yves Plancherel
    Abstract:

    A comparative analysis of the state and response of the latitude–depth meridional overturning Streamfunctions in the Climate Model Inter-comparison Project 3 (CMIP3) model set is presented. Simulated overturning strengths of the North Atlantic cell tend to converge towards observational estimates. The models whose simulations of the North Atlantic cell are closest to observational estimates indicate a 29.5 ± 13 % decrease in the maximum intensity of that cell by 2,100. In contrast, agreement with regard to the state and the response to anthropogenic radiative forcing of the global Southern Ocean abyssal cell is poor among the models. A weak relationship between the mean state and the response of the abyssal cell can be used to constrain the reduction of the Southern abyssal cell by 2,100 to 29.3 ± 20.7 %, in rough agreement with the decrease predicted in the Northern cell. The biases across the CMIP3 models in the Northern deep cell and Southern abyssal cell cannot be related dynamically by a buoyancy-based seesaw-like argument. The absence or presence of characteristic relationships between the state and evolution of different features of the overturning streamfunction indicate that the main reasons for across-model spread are how each model deals with subgrid-scale processes and viscosity. This highlights the fact that subgrid-scale parameterizations and resolution improvements should be a priority of model development. These factors are able to explain qualitatively the inter-model differences between the Northern overturning cells of the different models. Across-model differences in the winds over the Southern Ocean are responsible for much of the disparity in the overturning circulation cells of the Southern Ocean.

Jean-pierre Croisille - One of the best experts on this subject based on the ideXlab platform.

Shlomo Trachtenberg - One of the best experts on this subject based on the ideXlab platform.

  • A pure-compact scheme for the streamfunction formulation of Navier-Stokes equations
    Journal of Computational Physics, 2005
    Co-Authors: M Ben-artzi, D Fishelov, Jean-pierre Croisille, Shlomo Trachtenberg
    Abstract:

    A pure-streamfunction formulation is introduced for the numerical simulation of the two-dimensional incompressible Navier-Stokes equations. The idea is to replace the vorticity in the vorticity-streamfunction evolution equation by the Laplacian of the streamfunction. The resulting formulation includes the streamfunction only, thus no inter-function relations need to be invoked. A compact numerical scheme, which interpolates streamfunction values as well as its first order derivatives, is presented and analyzed. A number of numerical experiments are presented, including driven and double driven cavities, where the Reynolds numbers are sufficiently large, leading to symmetry breaking of asymptotic solutions.

M Ben-artzi - One of the best experts on this subject based on the ideXlab platform.