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Second-order Accurate (second-order + accurate)
Selected AbstractsA new family of generalized-, time integration algorithms without overshoot for structural dynamicsEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 12 2008Yu KaiPing Abstract A new family of generalized-, (G-,) algorithm without overshoot is presented by introducing seven free parameters into the single-step three-stage formulation for solution of structural dynamic problems. It is proved through finite difference analysis that these algorithms are unconditionally stable, second-order accurate and numerical dissipation controllable. The comparison of the new G-, algorithms with the commonly used G-, algorithms shows that the newly developed algorithms have the advantage of eliminating the overshooting characteristics exhibited by the commonly used algorithms while their excellent property of dissipation is preserved. The numerical simulation results obtained using a single-degree-of-freedom system and a two-degree-of-freedom system to represent the character of typical large systems coincide well with the results of theoretical analyses. Copyright © 2008 John Wiley & Sons, Ltd. [source] Optimal time integration parameters for elastodynamic contact problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2001A. Czekanski Abstract In this paper, we employ the generalized- , time integration scheme for treating elastodynamic contact problems. The criteria invoked for the selection of the four time integration parameters are motivated by our desire to ensure that the solution is unconditionally stable, second-order accurate, provides optimal high-frequency dissipation and preserves the energy and momentum transfer in dynamic rigid impact problems. New closed-form expressions for the time integration parameters are determined in terms of user-specified high-frequency spectral radius. The selected parameters help in avoiding the spurious high-frequency modes, which are present in the traditional Newmark method. Copyright © 2001 John Wiley & Sons, Ltd. [source] Simple and efficient integration of rigid rotations suitable for constraint solversINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2010Tomasz Koziara Abstract Simple and efficient way of integrating rigid rotations is presented. The algorithm is stable, second-order accurate, and in its explicit version involves evaluation of only two exponential maps per time step. The semi-explicit version of the proposed scheme improves upon the long-term stability, while it retains the explicitness in the force evaluation. The algebraic structure of both schemes makes them suitable forthe analysis of constrained multi-body systems. The explicit algorithm is specifically aimed at the analysis involving small incremental rotations, where its modest computational cost becomes the major advantage. The semi-explicit scheme naturally broadens the scope of possible applications. Copyright © 2009 John Wiley & Sons, Ltd. [source] A streamfunction,velocity approach for 2D transient incompressible viscous flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2010Jiten C. Kalita Abstract We recently proposed (J. Comput. Phys. 2005; 207(1):52,68) a new paradigm for solving the steady-state two-dimensional (2D) Navier,Stokes (N,S) equations using a streamfunction,velocity (,,v) formulation. This formulation was shown to avoid the difficulties associated with the traditional formulations (primitive variables and streamfunction-vorticity formulations). The new formulation was found to be second-order accurate and was found to yield accurate solutions of a number of fluid flow problems. In this paper, we extend the ideas and propose a second-order implicit, unconditionally stable ,,v formulation for the unsteady incompressible N,S equations. The method is used to solve several 2D time-dependent fluid flow problems, including the flow decayed by viscosity problem with analytical solution, the lid-driven square cavity problem, the backward-facing step problem and the flow past a square prism problem. For the problems with known exact solutions, our coarse grid transient solutions are extremely close to the analytical ones even for high Reynolds numbers (Re). For the driven cavity problem, our time-marching steady-state solutions up to Re=7500 provide excellent matches with established numerical results, and for Re=10000, our study concludes that the asymptotic stable solution is periodic as has been found by other authors in recent studies. For the backward step problem, our numerical results are in excellent agreement with established numerical and experimental results. Finally, for the flow past a square prism, we have very successfully simulated the von Kármán vortex street for Re=200. Copyright © 2009 John Wiley & Sons, Ltd. [source] Reducing numerical diffusion in interfacial gravity wave simulationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2005O. B. Fringer Abstract We demonstrate how the background potential energy is an excellent measure of the effective numerical diffusion or antidiffusion of an advection scheme by applying several advection schemes to a standing interfacial gravity wave. All existing advection schemes do not maintain the background potential energy because they are either diffusive, antidiffusive, or oscillatory. By taking advantage of the compressive nature of some schemes, which causes a decrease in the background potential energy, and the diffusive nature of others, which causes an increase in the background potential energy, we develop two background potential energy preserving advection schemes that are well-suited to study interfacial gravity waves at a density interface between two miscible fluids in closed domains such as lakes. The schemes employ total variation diminishing limiters and universal limiters in which the limiter is a function of both the upwind and local gradients as well as the background potential energy. The effectiveness of the schemes is validated by computing a sloshing interfacial gravity wave with a nonstaggered-grid Boussinesq solver, in which QUICK is employed for momentum and the pressure correction method is used, which is second-order accurate in time. For scalar advection, the present background potential energy preserving schemes are employed and compared to other TVD and non-TVD schemes, and we demonstrate that the schemes can control the change in the background potential energy due to numerical effects. Copyright © 2005 John Wiley & Sons, Ltd. [source] A parallel adaptive projection method for low Mach number flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1-2 2002J. B. Bell We describe an adaptive projection method for numerically simulating low Mach number flows. The projection method formulation enforces the velocity divergence constraint resulting from the low Mach number approximation. It is implemented on an adaptive hierarchy of logically rectangular grids, where each finer level is refined in space and in time. The adaptive algorithm has been shown in previous papers to be robust and second-order accurate, and to satisfy the principles of conservation and free-stream preservation as applicable. Here, the parallelization is described in some detail, and the methodology is demonstrated on two examples from premixed, low Mach number combustion. Published in 2002 by John Wiley & Sons, Ltd. [source] Some numerical properties of approaches to physics,dynamics coupling for NWPTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 614 2006Mark Dubal Abstract At the present time there exist a number of different approaches to the problem of coupling parametrized physical processes to the dynamical core in operational numerical weather-prediction (NWP) and climate models. Motivated by the various strategies in use, some idealized representative coupling schemes are constructed and subsequently analysed using a methodology in which the physics and dynamics terms are represented in a simplified way. Particular numerical properties of the idealized schemes which are of interest are the ability to capture correct steady-state solutions and to be second-order accurate in time. In general, the schemes require specific choices for the time-differencing of certain coupled processes if correct steady-state solutions are to be obtained. This has implications for the overall numerical stability of a coupling strategy. An alternative physics,dynamics coupling approach is then described and analysed. A multiple-sweep predictor,corrector coupling scheme is shown to capture the correct steady-state solution and to allow for second-order accuracy, provided that the convective process is coupled explicitly. This approach has a number of advantages over those currently used in operational NWP models. Copyright © 2006 Crown copyright [source] | ||||||||||