An Optimized Two-Step Hybrid Block Method Formulated in Variable Step-Size Mode for Integrating y′′=f(x,y,y′)y''=f(x,y,y') Numerically.

[EN]An optimized two-step hybrid block method is presented for integrating general second order initial value problems numerically. The method considers two intra-step points which are selected adequately in order to optimize the local truncation errors of the main formulas for the solution and the first derivative at the final point of the block. The new proposed method is consistent, zero-stable and has seventh algebraic order of convergence. To illustrate the performance of the method, some numerical experiments are presented for solving this kind of problems, in comparison with methods of similar characteristics in the literature

Approximate Periodic Solutions for Oscillatory Phenomena Modelled by Nonlinear Differential Equations

We apply the Fourier-least squares method (FLSM) which allows us to find approximate periodic solutions for a very general class of nonlinear differential equations modelling oscillatory phenomena. We illustrate the accuracy of the method by using several significant examples of nonlinear problems including the cubic Duffing oscillator, the Van der Pol oscillator, and the Jerk equations. The results are compared to those obtained by other methods

Coupling of time integration schemes for compressible unsteady flows

This work deals with the design of a hybrid time integrator that couples spatially explicit and implicit time integrators. In order to cope with the industrial solver of Ariane Group called FLUSEPA, the explicit scheme of Heun and the implicit scheme of Crank-Nicolson are hybridized using the transition parameter : the whole technique is called AION time integration. The latter is studied into details with special focus on spectral behaviour and on its ability to keep the accuracy. It is shown that the hybrid technique has interesting dissipation and dispersion properties while maintaining precision and avoiding spurious waves. Moreover, this hybrid approach is validated on several academic test cases for both convective and diffusive fluxes. And as expected the method is more interesting in term of computational time than standard time integrators. For the extension of this hybrid approach to the temporal adaptive method implemented in FLUSEPA, it was necessary to improve some treatments in order to maintain conservation and acceptable spectral properties. Finally the hybrid time integration was also applied to a RANS/LES turbulent test case with interesting computational time while capturing the flow physics

One and two dimensional space-energy flux synthesis with spatially discontinuous trial functions

The development of nuclear reactors as an energy source requires a substantial investment in capital and effort. This development depends heavily on accurate calculational methods. Space-energy flux synthesis, also variously called the spectral synthesis method, modal method, and overlapping group method, is one possible method. In this method the energy dependent flux is approximated by a superposition of energy trial functions (spectra). This thesis examines the use of this expansion in the context of diffusion theory. One and two dimensional diffusion theory codes have been written to accommodate a very general formulation of the spectral synthesis method. These codes use simultaneous solution methods to eliminate many of the convergence problems previously encountered with overlapping groups, while allowing a wide choice of interface conditions. Numerical experiments using these codes compare various choices of trial functions and types of weighting. A major portion of the investigation concerns the use of different sets of trial functions in different regions (spatially discontinuous trial functions). Particular attention is accorded to trial function and material interface conditions. Results favor conditions which preserve energy integrals of flux and current at interfaces

Safety and Reliability - Safe Societies in a Changing World

The contributions cover a wide range of methodologies and application areas for safety and reliability that contribute to safe societies in a changing world. These methodologies and applications include: - foundations of risk and reliability assessment and management - mathematical methods in reliability and safety - risk assessment - risk management - system reliability - uncertainty analysis - digitalization and big data - prognostics and system health management - occupational safety - accident and incident modeling - maintenance modeling and applications - simulation for safety and reliability analysis - dynamic risk and barrier management - organizational factors and safety culture - human factors and human reliability - resilience engineering - structural reliability - natural hazards - security - economic analysis in risk managemen