The Experts below are selected from a list of 116919 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.

Jan Fidler - One of the best experts on this subject based on the ideXlab platform.

  • relaxation times and Cell size in nonzero temperature micromagnetics
    Physica B-condensed Matter, 2006
    Co-Authors: M Kirschner, Gino Hrkac, Florian Dorfbauer, Dieter Suess, Thomas Schrefl, Jan Fidler
    Abstract:

    In nonzero-temperature micromagnetics the intrinsic magnetic parameters depend on the Computational Cell size. For large Cells the experimentally measured, only temperature dependent intrinsic properties can be used. For simulations on an atomistic level the experimentally measured zero-temperature values can be applied. In between, the intrinsic magnetic properties follow scaling laws which can be derived from Metropolis Monte Carlo simulations. Equilibrium magnetization states and thermally activated switching processes of small ferromagnetic cubes were calculated. With proper scaling of the material parameters the numerical results were found to be almost independent of the Computational Cell size.

  • Cell size corrections for nonzero temperature micromagnetics
    Journal of Applied Physics, 2005
    Co-Authors: M Kirschner, Gino Hrkac, Florian Dorfbauer, Dieter Suess, Thomas Schrefl, Jan Fidler
    Abstract:

    Micromagnetic calculations at nonzero temperatures depend on the Computational Cell size. This paper shows that the spontaneous magnetization MS of exchange-coupled moments has to be scaled by a Bloch-like law, which is similar to the well-known temperature dependence of MS. Using this scaling law, nonatomistic Metropolis Monte Carlo and stochastic Landau–Lifshitz–Gilbert simulations are performed in an external field of 0.1T. The error of the equilibrium magnetization at a temperature of T∕TC=0.38 and a Cell size of 1.5nm is then 0.9% as compared with atomistic calculations. In contrast, a Cell size-independent MS leads to an overestimation of the temperature of 3.2%.

Dochan Kwak - 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.

  • Numerical simulation of unsteady incompressible viscous flows in generalized coordinate systems
    11th International Conference on Numerical Methods in Fluid Dynamics, 1
    Co-Authors: Moshe Rossenfeld, Dochan Kwak
    Abstract:

    Several numerical solutions of the three dimensional unsteady incompressible Navier-Stokes equations in generalized coordinate systems are presented. The governing equations are discretized by finite volumes with special care to the accurate approximation of the geometric quantities. The unknowns are the pressure and the volume fluxes over the Computational Cell faces. This formulation results in a robust fractional step solution method for solving discrete equations. Although this method is formulated for the three dimensional case, only two dimensional unsteady results are given. Results are presented for a lid driven two dimensional cavity flow at Reynolds number of 10,000, and for the flow over a circular cylinder with vortex shedding for several Reynolds numbers in the range 100 less than Re less than 1000.

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.

Annette Volk - One of the best experts on this subject based on the ideXlab platform.

  • Theoretical Analysis of Computational Fluid Dynamics–Discrete Element Method Mathematical Model Solution Change With Varying Computational Cell Size
    Journal of Fluids Engineering, 2019
    Co-Authors: Annette Volk, Urmila Ghia
    Abstract:

    Successful verification and validation is crucial to build confidence in the application of coupled Computational fluid dynamics–discrete element method (CFD–DEM). Model verification includes ensuring a mesh-independent solution, which poses a major difficulty in CFD–DEM due to the complicated relationship between solution and Computational Cell size. In this paper, we investigate the production of numerical error in the CFD–DEM coupling procedure with Computational grid refinement. The porosity distribution output from simulations of fixed-particle beds is determined to be Gaussian, and the average and standard deviation of the representative distribution are reported against Cell size. We find that the standard deviation of bed porosity increases exponentially as the Cell size is reduced. The average drag calculated from each drag law is very sensitive to changes in the porosity standard deviation. When combined together, these effects result in an exponential change in expected drag force when the Cell size is small relative to the particle diameter. The divided volume fraction method of porosity calculation is shown to be superior to the centered volume fraction (CVF) method. The sensitivity of five popular drag laws to changes in the porosity distribution is presented, and the Ergun and Beetstra drag laws are shown to be the least sensitive to changes in the Cell size. A Cell size greater than three average particle diameters is recommended to prevent errors in the simulation results. A grid refinement study (GRS) is used to quantify numerical error.

  • Theoretical Analysis of CFD-DEM Mathematical Model Solution Change With Varying Computational Cell Size
    Volume 3: Fluid Machinery; Erosion Slurry Sedimentation; Experimental Multiscale and Numerical Methods for Multiphase Flows; Gas-Liquid Gas-Solid and , 2018
    Co-Authors: Annette Volk, Urmila Ghia
    Abstract:

    Successful verification and validation is crucial to build confidence in the application of coupled Computational Fluid Dynamics - Discrete Element Method (CFD-DEM). Model verification includes ensuring a mesh-independent solution, which poses a major difficulty in CFD-DEM due to the complicated solution relationship with Computational Cell size. In this paper, we investigate the theoretical relationship between the solution and Computational Cell size by tracing the effects of a change in Cell size through the mathematical model. The porosity profile for simulations of fixed-particle beds is determined to be Gaussian, and the average and standard deviation of the representative distribution are reported against Cell size. We find the standard deviation of bed porosity increases exponentially as the Cell size is reduced, and the drag calculations are very sensitive to changes in the porosity standard deviation, resulting in an exponential change in expected drag when the Cell size is small relative to the particle diameter. The divided volume fraction method of porosity calculation is shown to be superior to the centred volume fraction method, as it reduces the porosity standard deviation. The sensitivity of five popular drag laws to changes in the porosity profile is presented, and the Ergun and Beetstra drag laws are shown to be the least sensitive to changes in the Cell size.

  • Assessment of CFD-DEM solution error against Computational Cell size for flows through a fixed-bed of binary-sized particles
    Powder Technology, 2018
    Co-Authors: Annette Volk, Urmila Ghia, Gui Rong Liu
    Abstract:

    Abstract Computational Cell size is a crucial factor for accuracy in Computational Fluid Dynamics (CFD) - Discrete Element Method (DEM) simulations of particle-fluid interactions. In the present study, we investigate how simulation results change with Computational Cell size and mixture composition, for calculation of drag force over a fixed bed containing a binary-sized particle mixture. To investigate the complex solution convergence behavior, the simulation results are examined for several definitions of dimensionless Computational Cell size. Several regimes of consistent behavior, across three investigated mixtures, are identified and a consistently optimal Cell size range is identified. We find that both the difference between simulated solution results and published experimental results, and the standard deviation of the void fraction profile, show consistent trends when plotted against the dimensionless Computational Cell size based on the Sauter-mean particle diameter. Grid-refinement studies are performed across all grid solutions, and the Grid Convergence Index (GCI) is analyzed as a predictor for the grid solution error. Correlations between simulation error and GCI are not strong, likely because of incongruence of the solution trends with typical asymptotic convergence. Alternatively, a correlation between change in solution value on successively refined grids and finer-grid solution error is shown to be adequate for the current results.

  • Quantification of Numerical and Modeling Errors in Simulation of Fluid Flow Through a Fixed Particle Bed
    Volume 1B Symposia: Fluid Mechanics (Fundamental Issues and Perspectives; Industrial and Environmental Applications); Multiphase Flow and Systems (Mul, 2016
    Co-Authors: Annette Volk, Urmila Ghia, Christopher Gerold Stoltz, John Philip Hecht, Stamper Jason Allen
    Abstract:

    An open-source coupled Computational Fluid Dynamics (CFD) – Discrete Element Method (DEM), CFDEM, is employed to study flow through a fixed particle bed. The simulation is repeated for a range of Computational Cell sizes, and the solution trend is analyzed. A grid-refinement study procedure, standard for publication of CFD simulation results, is applied to the CFDEM simulations. The results are analyzed, with emphasis on the frequency of convergence and a comparison of the expected numerical error and extrapolated-solution error, termed the ‘offset’ method. Methods of analysis for numerical modeling parameters, as well as uniform reporting procedures, have not been established for granular-flow simulations. This has led to modeling errors and incorrect results that have hampered fluidization research. The present work shows that the standard grid-refinement study is applicable to granular-fluid flows, and produces results that are useful for common modeling choices such as drag correlation and determination of optimal Computational Cell size. Additional analysis procedures developed in this study, and based on the grid-refinement results, are shown to give good estimates of the resulting solution error.