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Splitting Method (splitting + method)

Distribution by Scientific Domains
Engineering75%

Kinds of Splitting Method

  • operator splitting method
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    Selected Abstracts

    Shoreline tracking and implicit source terms for a well balanced inundation model

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2010
    Giovanni FranchelloArticle first published online: 31 JUL 200
    Abstract The HyFlux2 model has been developed to simulate severe inundation scenario due to dam break, flash flood and tsunami-wave run-up. The model solves the conservative form of the two-dimensional shallow water equations using the finite volume method. The interface flux is computed by a Flux Vector Splitting method for shallow water equations based on a Godunov-type approach. A second-order scheme is applied to the water surface level and velocity, providing results with high accuracy and assuring the balance between fluxes and sources also for complex bathymetry and topography. Physical models are included to deal with bottom steps and shorelines. The second-order scheme together with the shoreline-tracking method and the implicit source term treatment makes the model well balanced in respect to mass and momentum conservation laws, providing reliable and robust results. The developed model is validated in this paper with a 2D numerical test case and with the Okushiri tsunami run up problem. It is shown that the HyFlux2 model is able to model inundation problems, with a satisfactory prediction of the major flow characteristics such as water depth, water velocity, flood extent, and flood-wave arrival time. The results provided by the model are of great importance for the risk assessment and management. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    A Rosenbrock-W method for real-time dynamic substructuring and pseudo-dynamic testing

    EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 9 2009
    C. P. Lamarche
    Abstract A variant of the Rosenbrock-W integration method is proposed for real-time dynamic substructuring and pseudo-dynamic testing. In this variant, an approximation of the Jacobian matrix that accounts for the properties of both the physical and numerical substructures is used throughout the analysis process. Only an initial estimate of the stiffness and damping properties of the physical components is required. It is demonstrated that the method is unconditionally stable provided that specific conditions are fulfilled and that the order accuracy can be maintained in the nonlinear regime without involving any matrix inversion while testing. The method also features controllable numerical energy dissipation characteristics and explicit expression of the target displacement and velocity vectors. The stability and accuracy of the proposed integration scheme are examined in the paper. The method has also been verified through hybrid testing performed of SDOF and MDOF structures with linear and highly nonlinear physical substructures. The results are compared with those obtained from the operator splitting method. An approach based on the modal decomposition principle is presented to predict the potential effect of experimental errors on the overall response during testing. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    The influences of thermophysical properties of porous media on superadiabatic combustion with reciprocating flow

    HEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 5 2006
    Liming Du
    Abstract The influences of thermophysical properties of porous media on superadiabatic combustion with reciprocating flow is numerically studied in order to improve the understanding of the complex heat transfer and optimum design of the combustor. The heat transfer performance of a porous media combustor strongly depends on the thermophysical properties of the porous material. In order to explore how the material properties influence reciprocating superadiabatic combustion of premixed gases in porous media (short for RSCP), a two-dimensional mathematical model of a simplified RSCP combustor is developed based on the hypothesis of local thermal non-equilibrium between the solid and the gas phases by solving separate energy equations for these two phases. The porous media is assumed to emit, absorb, and isotropically scatter radiation. The finite-volume method is used for computing radiation heat transfer processes. The flow and temperature fields are calculated by solving the mass, moment, gas and solid energy, and species conservation equations with a finite difference/control volume approach. Since the mass fraction conservation equations are stiff, an operator splitting method is used to solve them. The results show that the volumetric convective heat transfer coefficient and extinction coefficient of the porous media obviously affect the temperature distributions of the combustion chamber and burning speed of the gases, but thermal conductivity does not have an obvious effect. It indicates that convective heat transfer and heat radiation are the dominating ways of heat transfer, while heat conduction is a little less important. The specific heat of the porous media also has a remarkable impact on temperature distribution of gases and heat release rate. © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(5): 336,350, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20120 [source]

    Non-reflecting artificial boundaries for transient scalar wave propagation in a two-dimensional infinite homogeneous layer

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2003
    Chongbin Zhao
    Abstract This paper presents an exact non-reflecting boundary condition for dealing with transient scalar wave propagation problems in a two-dimensional infinite homogeneous layer. In order to model the complicated geometry and material properties in the near field, two vertical artificial boundaries are considered in the infinite layer so as to truncate the infinite domain into a finite domain. This treatment requires the appropriate boundary conditions, which are often referred to as the artificial boundary conditions, to be applied on the truncated boundaries. Since the infinite extension direction is different for these two truncated vertical boundaries, namely one extends toward x ,, and another extends toward x,- ,, the non-reflecting boundary condition needs to be derived on these two boundaries. Applying the variable separation method to the wave equation results in a reduction in spatial variables by one. The reduced wave equation, which is a time-dependent partial differential equation with only one spatial variable, can be further changed into a linear first-order ordinary differential equation by using both the operator splitting method and the modal radiation function concept simultaneously. As a result, the non-reflecting artificial boundary condition can be obtained by solving the ordinary differential equation whose stability is ensured. Some numerical examples have demonstrated that the non-reflecting boundary condition is of high accuracy in dealing with scalar wave propagation problems in infinite and semi-infinite media. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    A general Riemann solver for Euler equations

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2008
    Hao Wu
    Abstract In this paper, we present a general Riemann solver which is applied successfully to compute the Euler equations in fluid dynamics with many complex equations of state (EOS). The solver is based on a splitting method introduced by the authors. We add a linear advection term to the Euler equations in the first step, to make the numerical flux between cells easy to compute. The added linear advection term is thrown off in the second step. It does not need an iterative technique and characteristic wave decomposition for computation. This new solver is designed to permit the construction of high-order approximations to obtain high-order Godunov-type schemes. A number of numerical results show its robustness. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Numerical simulation of three-dimensional free surface flows

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2003
    V. Maronnier
    Abstract A numerical model is presented for the simulation of complex fluid flows with free surfaces in three space dimensions. The model described in Maronnier et al. (J. Comput. Phys. 1999; 155(2) : 439) is extended to three dimensional situations. The mathematical formulation of the model is similar to that of the volume of fluid (VOF) method, but the numerical procedures are different. A splitting method is used for the time discretization. At each time step, two advection problems,one for the predicted velocity field and the other for the volume fraction of liquid,are to be solved. Then, a generalized Stokes problem is solved and the velocity field is corrected. Two different grids are used for the space discretization. The two advection problems are solved on a fixed, structured grid made out of small cubic cells, using a forward characteristic method. The generalized Stokes problem is solved using continuous, piecewise linear stabilized finite elements on a fixed, unstructured mesh of tetrahedrons. The three-dimensional implementation is discussed. Efficient postprocessing algorithms enhance the quality of the numerical solution. A hierarchical data structure reduces memory requirements. Numerical results are presented for complex geometries arising in mold filling. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    Linear stability analysis and fourth-order approximations at first time level for the two space dimensional mildly quasi-linear hyperbolic equations

    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2001
    R. K. Mohanty
    Abstract In 1996, Mohanty et al. [1] presented a fourth-order finite difference solution of a two space dimensional nonlinear hyperbolic equation with Dirichlet boundary conditions. In 1998, Mohanty et al. [2] discussed a fourth-order approximation at first time level for the numerical solution of the one space dimensional hyperbolic equation. In both the cases, they have discussed the stability analysis for the linear hyperbolic equation having first-order space derivative terms. Recently, Mohanty et al. [3] have developed fourth-order difference formulas for the three space dimensional quasi-linear hyperbolic equations and obtained fourth-order approximation at first time level. In this article, we extend our strategy for solving the two space dimensional quasi-linear hyperbolic equation. An operator splitting method for a linear hyperbolic equation having a time derivative term is proposed. Linear stability analysis and fourth-order approximation at first time level for the two space dimensional quasi-linear hyperbolic equation are also discussed. The results of the numerical experiments are compared with the exact solution. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 607,618, 2001 [source]

    Three-dimensional numerical simulation of injection molding filling of optical lens and multiscale geometry using finite element method

    POLYMER ENGINEERING & SCIENCE, Issue 9 2006
    Sang-Woo Kim
    This article presents the development, verification, and validation of three-dimensional (3-D) numerical simulation for injection molding filling of 3-D parts and parts with microsurface features. For purpose of verification and comparison, two numerical models, the mixed model and the equal-order model, were used to solve the Stokes equations with three different tetrahedral elements (Taylor-Hood, MINI, and equal-order). The control volume scheme with tetrahedral finite element mesh was used for tracking advancing melt fronts and the operator splitting method was selected to solve the energy equation. A new, simple memory management procedure was introduced to deal with the large sparse matrix system without using a huge amount of storage space. The numerical simulation was validated for mold filling of a 3-D optical lens. The numerical simulation agreed very well with the experimental results and was useful in suggesting a better processing condition. As a new application area, a two-step macro,micro filling approach was adopted for the filling analysis of a part with a micro-surface feature to handle both macro and micro dimensions while avoiding an excessive number of elements. POLYM. ENG. SCI., 46:1263,1274, 2006. © 2006 Society of Plastics Engineers [source]