The Experts below are selected from a list of 189 Experts worldwide ranked by ideXlab platform

Marcel Vinokur - One of the best experts on this subject based on the ideXlab platform.

  • Development of a fractional-step method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems
    1992
    Co-Authors: Moshe Rosenfeld, Dochan Kwak, Marcel Vinokur
    Abstract:

    A fractional step method is developed for solving the time-dependent three-dimensional incompressible Navier-Stokes equations in generalized coordinate systems. The primitive variable formulation uses the pressure, defined at the center of the computational cell, and the volume fluxes across the faces of the cells as the dependent variables, instead of the Cartesian components of the Velocity. This choice is equivalent to using the Contravariant Velocity components in a staggered grid multiplied by the volume of the computational cell. The governing equations are discretized by finite volumes using a staggered mesh system. The solution of the continuity equation is decoupled from the momentum equations by a fractional step method which enforces mass conservation by solving a Poisson equation. This procedure, combined with the consistent approximations of the geometric quantities, is done to satisfy the discretized mass conservation equation to machine accuracy, as well as to gain the favorable convergence properties of the Poisson solver. The momentum equations are solved by an approximate factorization method, and a novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two- and three-dimensional laminar test cases are computed and compared with other numerical and experimental results to validate the solution method. Good agreement is obtained in all cases.

  • A fractional step solution method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems
    Journal of Computational Physics, 1991
    Co-Authors: Moshe Rosenfeld, Dochan Kwak, Marcel Vinokur
    Abstract:

    Abstract A fractional step method is developed for solving the time-dependent three-dimensional incompressible Navier-Stokes equations in generalized coordinate systems. The primitive variable formulation uses the pressure, defined at the center of the computational cell, and the volume fluxes across the faces of the cells as the dependent variables, instead of the Cartesian components of the Velocity. This choice is equivalent to using the Contravariant Velocity components in a staggered grid multiplied by the volume of the computational cell. The governing equations are discretized by finite volumes using a staggered mesh system. The solution of the continuity equation is decoupled from the momentum equations by a fractional step method which enforces mass conservation by solving a Poisson equation. This procedure, combined with a consistent approximation of the geometric quantities, is done to satisfy the discretized mass conservation equation to machine accuracy, as well as to gain the favorable convergence properties of the Poisson solver. The momentum equations are solved by an approximate factorization method, and a novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two- and three-dimensional laminar test cases are computed and compared with other numerical and experimental results to validate the solution method. Good agreement is obtained in all cases.

Dochan Kwak - One of the best experts on this subject based on the ideXlab platform.

  • Definition of Contravariant Velocity Components
    2002
    Co-Authors: Ching-mao Hung, Dochan Kwak
    Abstract:

    This is an old issuein computational fluid dynamics (CFD). What is the so-called Contravariant Velocity or cortravariant Velocity component? In the article, we review the basicsof tensor analysis and give the Contravariant Velocity componenta rigorous explanation. For a given coordin._tesystem, there exist two uniquely determined sets of base vector systems- oneis the c_)variantand another is the Contravariant basevector system. The two base vector systens are reciprocal. The so-called Contravariant Velocity component is really the contraworiantcomponentof a Velocity vector for a time-independent coordinatesystem, or the co_travariant componentof a relative Velocity betweenfluid and coordinates, for a time-depeadentcoordinate system. The Contravariant Velocity components arenot physicalquantities of the Velocity vector. Their magnitudes, dimensions, and associated directions are controlled by their corresponding covariant base vectors. Several 2-D linear examples and 2-E mass-conservation equation are used to illustrate the details of expressing a vector with r,_spect to the covariant and Contravariant base vector systems, respectively.

  • Development of a fractional-step method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems
    1992
    Co-Authors: Moshe Rosenfeld, Dochan Kwak, Marcel Vinokur
    Abstract:

    A fractional step method is developed for solving the time-dependent three-dimensional incompressible Navier-Stokes equations in generalized coordinate systems. The primitive variable formulation uses the pressure, defined at the center of the computational cell, and the volume fluxes across the faces of the cells as the dependent variables, instead of the Cartesian components of the Velocity. This choice is equivalent to using the Contravariant Velocity components in a staggered grid multiplied by the volume of the computational cell. The governing equations are discretized by finite volumes using a staggered mesh system. The solution of the continuity equation is decoupled from the momentum equations by a fractional step method which enforces mass conservation by solving a Poisson equation. This procedure, combined with the consistent approximations of the geometric quantities, is done to satisfy the discretized mass conservation equation to machine accuracy, as well as to gain the favorable convergence properties of the Poisson solver. The momentum equations are solved by an approximate factorization method, and a novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two- and three-dimensional laminar test cases are computed and compared with other numerical and experimental results to validate the solution method. Good agreement is obtained in all cases.

  • A fractional step solution method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems
    Journal of Computational Physics, 1991
    Co-Authors: Moshe Rosenfeld, Dochan Kwak, Marcel Vinokur
    Abstract:

    Abstract A fractional step method is developed for solving the time-dependent three-dimensional incompressible Navier-Stokes equations in generalized coordinate systems. The primitive variable formulation uses the pressure, defined at the center of the computational cell, and the volume fluxes across the faces of the cells as the dependent variables, instead of the Cartesian components of the Velocity. This choice is equivalent to using the Contravariant Velocity components in a staggered grid multiplied by the volume of the computational cell. The governing equations are discretized by finite volumes using a staggered mesh system. The solution of the continuity equation is decoupled from the momentum equations by a fractional step method which enforces mass conservation by solving a Poisson equation. This procedure, combined with a consistent approximation of the geometric quantities, is done to satisfy the discretized mass conservation equation to machine accuracy, as well as to gain the favorable convergence properties of the Poisson solver. The momentum equations are solved by an approximate factorization method, and a novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two- and three-dimensional laminar test cases are computed and compared with other numerical and experimental results to validate the solution method. Good agreement is obtained in all cases.

Hisaaki Daiguji - One of the best experts on this subject based on the ideXlab platform.

  • COMPUTATION OF UNSTEADY TRANSONIC CASCADE FLOW USING THE EULER AND NAVIER-STOKES EQUATIONS OF Contravariant VELOCITIES
    JSME International Journal Series B, 1994
    Co-Authors: Satoru Yamamoto, Hisaaki Daiguji
    Abstract:

    The purpose of the present paper is to investigate the steady and unsteady flows through subsonic and transonic turbine cascades using the Euler and Navier-Stokes (N-S) solvers developed by the authors. Use of the fundamental equations of Contravariant Velocity components also proposed by the authors is very convenient for treating several kinds of boundary conditions. Some efficient numerical schemes for the unsteady calculation, shock capturing and turbulent quantities are also developed. As numerical examples, we show the numerical results of some turbine cascade flows by assuming the flows to be inviscid or viscous (turbulent) and steady or unsteady. The results are compared with each other and with the experimental data. Finally, the reliability and the limitation of the present numerical solvers for the turbine cascade cases are discussed.

  • Application of an implicit time-marching scheme to a three-dimensional incompressible flow problem in curvilinear coordinate systems
    Computers & Fluids, 1992
    Co-Authors: Toshiaki Ikohagi, Byeong Rog Shin, Hisaaki Daiguji
    Abstract:

    Abstract An implicit finite-difference scheme based on the SMAC method for solving steady three-dimensional incompressible viscous flows is proposed. The three-dimensional incompressible Navier-Stokes equations in general curvilinear coordinates, in which the Contravariant velocities and the pressure are used as the unknown variables, have been derived by the authors. The momentum equations for the Contravariant Velocity components and the elliptic equation for the pressure are solved directly in the transformed space by applying the delta-form approximate-factorization scheme and the Tschebyscheff SLOR method, respectively. The present implicit scheme is stable under correctly imposed boundary conditions, since the spurious error and the numerical instabilities can be suppressed by satisfying the continuity condition identically, and by employing the staggered grid and the TVD upwind scheme. Some numerical results for three-dimensional flow over a backward-facing step are shown to demonstrate the reliability of the present scheme and to clarify the three-dimensional effects of such complex flows.

  • An implicit time-marching method for solving the 3-D compressible Euler equations
    Tenth International Conference on Numerical Methods in Fluid Dynamics, 1
    Co-Authors: Hisaaki Daiguji, Yasuo Motohashi, Satoru Yamamoto
    Abstract:

    An implicit time-marching method for analysing steady three-dimensional inviscid transonic flow problems has been proposed. This method is based on the well-known Beam-Warming delta-form approximate-factorization scheme, and improved in the following points. (i) In order to treat the solid wall boundary condition without difficulty, the momentum equations of Contravariant Velocity as the fundamental equations in curvilinear coordiantes are used. (ii) To save the computer time and to increase the stability, the existing techniques of diagonalization and upstreaming are applied. Some and implicit versions of the present method have been proposed. These methods are easily extended to the viscious flow problems.

Moshe Rosenfeld - One of the best experts on this subject based on the ideXlab platform.

  • Development of a fractional-step method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems
    1992
    Co-Authors: Moshe Rosenfeld, Dochan Kwak, Marcel Vinokur
    Abstract:

    A fractional step method is developed for solving the time-dependent three-dimensional incompressible Navier-Stokes equations in generalized coordinate systems. The primitive variable formulation uses the pressure, defined at the center of the computational cell, and the volume fluxes across the faces of the cells as the dependent variables, instead of the Cartesian components of the Velocity. This choice is equivalent to using the Contravariant Velocity components in a staggered grid multiplied by the volume of the computational cell. The governing equations are discretized by finite volumes using a staggered mesh system. The solution of the continuity equation is decoupled from the momentum equations by a fractional step method which enforces mass conservation by solving a Poisson equation. This procedure, combined with the consistent approximations of the geometric quantities, is done to satisfy the discretized mass conservation equation to machine accuracy, as well as to gain the favorable convergence properties of the Poisson solver. The momentum equations are solved by an approximate factorization method, and a novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two- and three-dimensional laminar test cases are computed and compared with other numerical and experimental results to validate the solution method. Good agreement is obtained in all cases.

  • A fractional step solution method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems
    Journal of Computational Physics, 1991
    Co-Authors: Moshe Rosenfeld, Dochan Kwak, Marcel Vinokur
    Abstract:

    Abstract A fractional step method is developed for solving the time-dependent three-dimensional incompressible Navier-Stokes equations in generalized coordinate systems. The primitive variable formulation uses the pressure, defined at the center of the computational cell, and the volume fluxes across the faces of the cells as the dependent variables, instead of the Cartesian components of the Velocity. This choice is equivalent to using the Contravariant Velocity components in a staggered grid multiplied by the volume of the computational cell. The governing equations are discretized by finite volumes using a staggered mesh system. The solution of the continuity equation is decoupled from the momentum equations by a fractional step method which enforces mass conservation by solving a Poisson equation. This procedure, combined with a consistent approximation of the geometric quantities, is done to satisfy the discretized mass conservation equation to machine accuracy, as well as to gain the favorable convergence properties of the Poisson solver. The momentum equations are solved by an approximate factorization method, and a novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two- and three-dimensional laminar test cases are computed and compared with other numerical and experimental results to validate the solution method. Good agreement is obtained in all cases.

N. Kashimura - One of the best experts on this subject based on the ideXlab platform.

  • Numerical Simulation of the Flow involving the Free Surface using the Generalized Coordinate System
    Computational Mechanics ’95, 1995
    Co-Authors: T. Sakuragi, N. Kashimura
    Abstract:

    A computational program for solving the unsteady incompressible viscous flow with free surface in generalized coordinate system was developed using the upwind control volume scheme. The momentum equations descrived by the Contravariant Velocity components and the Poisson equation for the pressure are solved by a SMAC like time- martching scheme. An adaptation of the well-known VOF algorithm to generalized coordinates is used to investigate free surface. As numerical examples, the flow pattern of the water under gravity in U-type duct, and the flow of the water filling in a square containing four blocks were simulated. In comparison with the experimental data by the image processing, the numerical result of the flow pattern in a cavity shows a good qualitative agreement despite being a two dimensional calculation.