A generalized approach for implicit time integration of piecewise linear/nonlinear systems

Engine fan blade-off (FBO) is an extreme event that could well place the flight safety at risk. When it happens, the engine will experience high-velocity impact at first, and then enter into a “high-power” stage due to huge unbalance before coming to a steady state called “windmilling”. The analytical process for FBO can be split into two phases, one for impact simulation and the other for obtaining the FBO load to pylon. Typically, explicit method with fine mesh finite elements is used in the first phase, and implicit method with coarse meshes is adopted in the second one. In most cases, the only connection between these two analyses may be the unbalance level caused by FBO. More structural responses other than the unbalance level due to fan blade impact are actually ignored in the succeeding implicit analysis. Attempts have been made by Boeing, GE and MSC to integrate these two processes by adding some features in MD Nastran. Yet the intermediate binary files created and the restricted input entries make the integration process quite inflexible. This paper introduces an explicit-implicit time integration approach for finite element analysis of engine load following an FBO event. The proposed method attempts to connect the two stages more closely, yet in a more flexible manner. In this approach, the engine structural response under FBO obtained from explicit analysis is transferred to the implicit analysis, together with the unbalance level caused by blade loss. The necessity of the approach is discussed, and sensitivity analysis is conducted to understand the factors that play significant roles in the approach. As the models for explicit and implicit analyses are different in mesh sizes and scales, the authors also develop a tool that can interpolate the load information and further, smooth it to fit calculation. Finally, the approach is tested on a full engine model to show its applicability and advantages over the traditional method for load evaluation of FBO event.

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High-Order Locally Implicit Time Integration Strategies in a Discontinuous Galerkin Method for Maxwell’s Equations

Lecture Notes in Computational Science and Engineering - Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012 ◽

10.1007/978-3-319-01601-6_16 ◽

2013 ◽

pp. 205-215 ◽

Cited By ~ 1

Author(s):

S. Descombes ◽

S. Lanteri ◽

L. Moya

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Maxwell’S Equations ◽

Maxwell's Equations ◽

Time Integration ◽

High Order ◽

Implicit Time ◽

Implicit Time Integration ◽

Integration Strategies

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Impact of difference between explicit and implicit second-order time integration schemes on isotropic/anisotropic steady incompressible turbulence field

Journal of Physics Conference Series ◽

10.1088/1742-6596/2090/1/012145 ◽

2021 ◽

Vol 2090 (1) ◽

pp. 012145

Author(s):

Ryuma Honda ◽

Hiroki Suzuki ◽

Shinsuke Mochizuki

Keyword(s):

Kinetic Energy ◽

Energy Conservation ◽

Integration Method ◽

Time Integration ◽

Second Order ◽

Implicit Time ◽

Explicit Time Integration ◽

Time Integration Method ◽

Implicit Time Integration ◽

Time Integration Methods

Abstract This study presents the impact of the difference between the implicit and explicit time integration methods on a steady turbulent flow field. In contrast to the explicit time integration method, the implicit time integration method may produce significant kinetic energy conservation error because the widely used spatial difference method for discretizing the governing equations is explicit with respect to time. In this study, the second-order Crank-Nicolson method is used as the implicit time integration method, and the fourth-order Runge-Kutta, second-order Runge-Kutta and second-order Adams-Bashforth methods are used as explicit time integration methods. In the present study, both isotropic and anisotropic steady turbulent fields are analyzed with two values of the Reynolds number. The turbulent kinetic energy in the steady turbulent field is hardly affected by the kinetic energy conservation error. The rms values of static pressure fluctuation are significantly sensitive to the kinetic energy conservation error. These results are examined by varying the time increment value. These results are also discussed by visualizing the large scale turbulent vortex structure.

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