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Fractional Step Method (fractional + step_method)
Selected AbstractsImprovement of mass source/sink for an immersed boundary methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2007Wei-Xi Huang Abstract An improved immersed boundary method using a mass source/sink as well as momentum forcing is developed for simulating flows over or inside complex geometries. The present method is based on the Navier,Stokes solver adopting the fractional step method and a staggered Cartesian grid system. A more accurate formulation of the mass source/sink is derived by considering mass conservation of the virtual cells in the fluid crossed by the immersed boundary. Two flow problems (the decaying vortex problem and uniform flow past a circular cylinder) are used to validate the proposed formulation. The results indicate that the accuracy near the immersed boundary is improved by introducing the accurate mass source/sink. Copyright © 2006 John Wiley & Sons, Ltd. [source] A high-order mass-lumping procedure for B-spline collocation method with application to incompressible flow simulationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2003O. Botella Abstract This paper presents new developments of the staggered spline collocation method for cost-effective solution to the incompressible Navier,Stokes equations. Maximal decoupling of the velocity and the pressure is obtained by using the fractional step method of Gresho and Chan, allowing the solution to sparse elliptic problems only. In order to preserve the high-accuracy of the B-spline method, this fractional step scheme is used in association with a sparse approximation to the inverse of the consistent mass matrix. Such an approximation is constructed from local spline interpolation method, and represents a high-order generalization of the mass-lumping technique of the finite-element method. A numerical investigation of the accuracy and the computational efficiency of the resulting semi-consistent spline collocation schemes is presented. These schemes generate a stable and accurate unsteady Navier,Stokes solver, as assessed by benchmark computations. Copyright © 2003 John Wiley & Sons, Ltd. [source] Three-dimensional numerical modelling of free surface flows with non-hydrostatic pressureINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2002Musteyde B. Koçyigit Abstract A three-dimensional numerical model is developed for incompressible free surface flows. The model is based on the unsteady Reynolds-averaged Navier,Stokes equations with a non-hydrostatic pressure distribution being incorporated in the model. The governing equations are solved in the conventional sigma co-ordinate system, with a semi-implicit time discretization. A fractional step method is used to enable the pressure to be decomposed into its hydrostatic and hydrodynamic components. At every time step one five-diagonal system of equations is solved to compute the water elevations and then the hydrodynamic pressure is determined from a pressure Poisson equation. The model is applied to three examples to simulate unsteady free surface flows where non-hydrostatic pressures have a considerable effect on the velocity field. Emphasis is focused on applying the model to wave problems. Two of the examples are about modelling small amplitude waves where the hydrostatic approximation and long wave theory are not valid. The other example is the wind-induced circulation in a closed basin. The numerical solutions are compared with the available analytical solutions for small amplitude wave theory and very good agreement is obtained. Copyright © 2002 John Wiley & Sons, Ltd. [source] UNSTEADY STATE DISPERSION OF AIR POLLUTANTS UNDER THE EFFECTS OF DELAYED AND NONDELAYED REMOVAL MECHANISMSNATURAL RESOURCE MODELING, Issue 4 2009MANJU AGARWAL Abstract In this paper, we present a two-dimensional time-dependent mathematical model for studying the unsteady state dispersion of air pollutants emitted from an elevated line source in the atmosphere under the simultaneous effects of delayed (slow) and nondelayed (instantaneous) removal mechanisms. The wind speed and coefficient of diffusion are taken as functions of the vertical height above the ground. The deposition of pollutants on the absorptive ground and leakage into the atmosphere at the inversion layer are also included in the model by applying appropriate boundary conditions. The model is solved numerically by the fractional step method. The Lagrangian approach is used to solve the advection part, whereas the Eulerian finite difference scheme is applied to solve the part with the diffusion and removal processes. The solutions are analyzed to observe the effects of coexisting delayed and nondelayed removal mechanisms on overall dispersion. Comparison of delayed and nondelayed removal processes of equal capacity shows that the latter (nondelayed) process is more effective than the former (delayed removal) in the removal of pollutants from the atmosphere. [source] A new update procedure for internal variables in an ALE-description of rolling contactPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005M. Ziefle In FEM analysis of rolling contact problems Arbitrary Lagrangian-Eulerian (ALE) methods are the state of the art. These methods allow mesh refinements concentrated to the contact region and offer a time independent formulation of stationary elastic rolling. The relative-kinematic description of rolling leads to a relative motion between the finite element mesh and the material points. Thus in the case of inelastic material behavior history dependent constitutive equations contain convective terms. The handling of these convective terms is performed by a so called fractional step method. A material step is followed by a convection step. In the first step the nonlinear solid contact problem is resolved by neglecting the convective terms. In the following step the internal variables are transported on the streamlines of the material particles by solving the advection equation via a time-discontinuous Galerkin method. This update procedure is demonstrated on a typical FEM-tire model. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||