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Temporal Discretization (temporal + discretization)
Selected AbstractsRapid simulated hydrologic response within the variably saturated near surfaceHYDROLOGICAL PROCESSES, Issue 3 2008Brian A. Ebel Abstract Column and field experiments have shown that the hydrologic response to increases in rainfall rates can be more rapid than expected from simple estimates. Physics-based hydrologic response simulation, with the Integrated Hydrology Model (InHM), is used here to investigate rapid hydrologic response, within the variably saturated near surface, to temporal variations in applied flux at the surface boundary. The factors controlling the speed of wetting front propagation are discussed within the Darcy,Buckingham conceptual framework, including kinematic wave approximations. The Coos Bay boundary-value problem is employed to examine simulated discharge, pressure head, and saturation responses to a large increase in applied surface flux. The results presented here suggest that physics-based simulations are capable of representing rapid hydrologic response within the variably saturated near surface. The new InHM simulations indicate that the temporal discretization and measurement precision needed to capture the rapid subsurface response to a spike increase in surface flux, necessary for both data-based analyses and evaluation of physics-based models, are smaller than the capabilities of the instrumentation deployed at the Coos Bay experimental catchment. Copyright © 2007 John Wiley & Sons, Ltd. [source] Kalman filter finite element method applied to dynamic ground motionINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2009Yusuke Kato Abstract The purpose of this paper is to investigate the estimation of dynamic elastic behavior of the ground using the Kalman filter finite element method. In the present paper, as the state equation, the balance of stress equation, the strain,displacement equation and the stress,strain equation are used. For temporal discretization, the Newmark ¼ method is employed, and for the spatial discretization the Galerkin method is applied. The Kalman filter finite element method is a combination of the Kalman filter and the finite element method. The present method is adaptable to estimations not only in time but also in space, as we have confirmed by its application to the Futatsuishi quarry site. The input data are the measured velocity, acceleration, etc., which may include mechanical noise. It has been shown in numerical studies that the estimated velocity, acceleration, etc., at any other spatial and temporal point can be obtained by removing the noise included in the observation. Copyright © 2008 John Wiley & Sons, Ltd. [source] Interface tracking finite volume method for complex solid,fluid interactions on fixed meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2002H. S. Udaykumar Abstract We present a numerical technique for computing flowfields around moving solid boundaries immersed in fixed meshes. The mixed Eulerian,Lagrangian framework treats the immersed boundaries as sharp solid,fluid interfaces and a conservative finite volume formulation allows boundary conditions at the moving surfaces to be exactly applied. A semi-implicit second-order accurate spatial and temporal discretization is employed with a fractional-step scheme for solving the flow equations. A multigrid accelerator for the pressure Poisson equations has been developed to apply in the presence of multiple embedded solid regions on the mesh. We present applications of the method to two types of problems: (a) solidification in the presence of flows and particles, (b) fluid,structure interactions in flow control. In both these problems, the sharp interface method presents advantages by being able to track arbitrary interface motions, while capturing the full viscous, unsteady dynamics. Copyright © 2001 John Wiley & Sons, Ltd. [source] Temporal accuracy analysis of phase change convection simulations using the JFNK-SIMPLE algorithmINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2007Katherine J. Evans Abstract The incompressible Navier,Stokes and energy conservation equations with phase change effects are applied to two benchmark problems: (1) non-dimensional freezing with convection; and (2) pure gallium melting. Using a Jacobian-free Newton,Krylov (JFNK) fully implicit solution method preconditioned with the SIMPLE (Numerical Heat Transfer and Fluid Flow. Hemisphere: New York, 1980) algorithm using centred discretization in space and three-level discretization in time converges with second-order accuracy for these problems. In the case of non-dimensional freezing, the temporal accuracy is sensitive to the choice of velocity attenuation parameter. By comparing to solutions with first-order backward Euler discretization in time, it is shown that the second-order accuracy in time is required to resolve the fine-scale convection structure during early gallium melting. Qualitative discrepancies develop over time for both the first-order temporal discretized simulation using the JFNK-SIMPLE algorithm that converges the nonlinearities and a SIMPLE-based algorithm that converges to a more common mass balance condition. The discrepancies in the JFNK-SIMPLE simulations using only first-order rather than second-order accurate temporal discretization for a given time step size appear to be offset in time. Copyright © 2007 John Wiley & Sons, Ltd. [source] Finite-element/level-set/operator-splitting (FELSOS) approach for computing two-fluid unsteady flows with free moving interfacesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2005Anton Smolianski Abstract The present work is devoted to the study on unsteady flows of two immiscible viscous fluids separated by free moving interface. Our goal is to elaborate a unified strategy for numerical modelling of two-fluid interfacial flows, having in mind possible interface topology changes (like merger or break-up) and realistically wide ranges for physical parameters of the problem. The proposed computational approach essentially relies on three basic components: the finite element method for spatial approximation, the operator-splitting for temporal discretization and the level-set method for interface representation. We show that the finite element implementation of the level-set approach brings some additional benefits as compared to the standard, finite difference level-set realizations. In particular, the use of finite elements permits to localize the interface precisely, without introducing any artificial parameters like the interface thickness; it also allows to maintain the second-order accuracy of the interface normal, curvature and mass conservation. The operator-splitting makes it possible to separate all major difficulties of the problem and enables us to implement the equal-order interpolation for the velocity and pressure. Diverse numerical examples including simulations of bubble dynamics, bifurcating jet flow and Rayleigh,Taylor instability are presented to validate the computational method. Copyright © 2004 John Wiley & Sons, Ltd. [source] Higher order explicit time integration schemes for Maxwell's equationsINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 5-6 2002Holger Spachmann Abstract The finite integration technique (FIT) is an efficient and universal method for solving a wide range of problems in computational electrodynamics. The conventional formulation in time-domain (FITD) has a second-order accuracy with respect to spatial and temporal discretization and is computationally equivalent with the well-known finite difference time-domain (FDTD) scheme. The dispersive character of the second-order spatial operators and temporal integration schemes limits the problem size to electrically small structures. In contrast higher-order approaches result not only in low-dispersive schemes with modified stability conditions but also higher computational costs. In this paper, a general framework of explicit Runge,Kutta and leap-frog integrators of arbitrary orders N is derived. The powerful root-locus method derived from general system theory forms the basis of the theoretical mainframe for analysing convergence, stability and dispersion characteristics of the proposed integrators. As it is clearly stated, the second- and fourth-order leap-frog scheme are highly preferable in comparison to any other higher order Runge,Kutta or leap-frog scheme concerning stability, efficiency and energy conservation. Copyright © 2002 John Wiley & Sons, Ltd. [source] Optimal operation of GaN thin film epitaxy employing control vector parametrizationAICHE JOURNAL, Issue 4 2006Amit Varshney Abstract An approach that links nonlinear model reduction techniques with control vector parametrization-based schemes is presented, to efficiently solve dynamic constraint optimization problems arising in the context of spatially-distributed processes governed by highly-dissipative nonlinear partial-differential equations (PDEs), utilizing standard nonlinear programming techniques. The method of weighted residuals with empirical eigenfunctions (obtained via Karhunen-Loève expansion) as basis functions is employed for spatial discretization together with control vector parametrization formulation for temporal discretization. The stimulus for the earlier approach is provided by the presence of low order dominant dynamics in the case of highly dissipative parabolic PDEs. Spatial discretization based on these few dominant modes (which are elegantly captured by empirical eigenfunctions) takes into account the actual spatiotemporal behavior of the PDE which cannot be captured using finite difference or finite element techniques with a small number of discretization points/elements. The proposed approach is used to compute the optimal operating profile of a metallorganic vapor-phase epitaxy process for the production of GaN thin films, with the objective to minimize the spatial nonuniformity of the deposited film across the substrate surface by adequately manipulating the spatiotemporal concentration profiles of Ga and N precursors at the reactor inlet. It is demonstrated that the reduced order optimization problem thus formulated using the proposed approach for nonlinear order reduction results in considerable savings of computational resources and is simultaneously accurate. It is demonstrated that by optimally changing the precursor concentration across the reactor inlet it is possible to reduce the thickness nonuniformity of the deposited film from a nominal 33% to 3.1%. © 2005 American Institute of Chemical Engineers AIChE J, 2006 [source] A monotonically-damping second-order-accurate unconditionally-stable numerical scheme for diffusionTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 627 2007Nigel Wood Abstract We present a new two-step temporal discretization of the diffusion equation, which is formally second-order-accurate and unconditionally stable. A novel aspect of the scheme is that it is monotonically damping: the damping rate is a monotonically-increasing function of the diffusion coefficient, independent of the size of the time step, when the diffusion coefficient is independent of the variable being diffused. Furthermore, the damping rate increases without bound as the diffusion coefficient similarly increases. We discuss the nonlinear behaviour of the scheme when the diffusion coefficient is a function of the diffused variable. The scheme is designed to maintain any steady-state solution. We present examples of the performance of the scheme. © Crown Copyright 2007. Reproduced with the permission of the Controller of HMSO. Published by John Wiley & Sons, Ltd. [source] A space,time discontinuous Galerkin method for the solution of the wave equation in the time domainINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2009Steffen Petersen Abstract In recent years, the focus of research in the field of computational acoustics has shifted to the medium frequency regime and multiscale wave propagation. This has led to the development of new concepts including the discontinuous enrichment method. Its basic principle is the incorporation of features of the governing partial differential equation in the approximation. In this contribution, this concept is adapted for the simulation of transient problems governed by the wave equation. We present a space,time discontinuous Galerkin method with Lagrange multipliers, where the shape approximation in space and time is based on solutions of the homogeneous wave equation. The use of hierarchical wave-like basis functions is enabled by means of a variational formulation that allows for discontinuities in both the spatial and the temporal discretizations. Numerical examples in one space dimension demonstrate the outstanding performance of the proposed method compared with conventional space,time finite element methods. Copyright © 2008 John Wiley & Sons, Ltd. [source] Examination for adjoint boundary conditions in initial water elevation estimation problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2010T. KurahashiArticle first published online: 23 JUL 200 Abstract I present here a method of generating a distribution of initial water elevation by employing the adjoint equation and finite element methods. A shallow-water equation is employed to simulate flow behavior. The adjoint equation method is utilized to obtain a distribution of initial water elevation for the observed water elevation. The finite element method, using the stabilized bubble function element, is used for spatial discretization, and the Crank,Nicolson method is used for temporal discretizations. In addition to a method for optimally assimilating water elevation, a method is presented for determining adjoint boundary conditions. An examination using the observation data including noise data is also carried out. Copyright © 2009 John Wiley & Sons, Ltd. [source] | ||||||||||