Step Approximation for Water Wave Scattering by Multiple Thin Barriers over Undulated Bottoms

This paper investigates the scattering of oblique water waves by multiple thin barriers over undulation bottoms using the eigenfunction matching method (EMM). In the solution procedures of the EMM, the bottom topographies are sliced into shelves separated by steps. On each step, surface-piercing or/and bottom-standing barriers can be presented or not. For each shelf, the solution is composed of eigenfunctions with unknown coefficients representing the wave amplitudes. Then applying the conservations of mass and momentum, a system of linear equations is resulted and can be solved by a sparse-matrix solver. If no barriers are presented on the steps, the proposed EMM formulation degenerates to the water wave scattering over undulating bottoms. The effects on the barrier lengths, barrier positions and oblique wave incidences by different undulated bottoms are studied. In addition, the EMM is also applied to solve the Bragg reflections of normal and oblique water waves by periodic barrier over sinusoidal bottoms. The accuracy of the solution is demonstrated by comparing it with the results in the literature.

Reliability-Based Design Optimization of Structures Using Complex-Step Approximation with Sensitivity Analysis

Structural optimization aims to achieve a structural design that provides the best performance while satisfying the given design constraints. When uncertainties in design and conditions are taken into account, reliability-based design optimization (RBDO) is adopted to identify solutions with acceptable failure probabilities. This paper outlines a method for sensitivity analysis, reliability assessment, and RBDO for structures. Complex-step (CS) approximation and the first-order reliability method (FORM) are unified in the sensitivity analysis of a probabilistic constraint, which streamlines the setup of optimization problems and enhances their implementation in RBDO. Complex-step approximation utilizes an imaginary number as a step size to compute the first derivative without subtractive cancellations in the formula, which have been observed to significantly affect the accuracy of calculations in finite difference methods. Thus, the proposed method can select a very small step size for the first derivative to minimize truncation errors, while achieving accuracy within the machine precision. This approach integrates complex-step approximation into the FORM to compute sensitivity and assess reliability. The proposed method of RBDO is tested on structural optimization problems across a range of statistical variations, demonstrating that performance benefits can be achieved while satisfying precise probabilistic constraints.

Research on Coupling Scheme of Monte Carlo Burnup Calculation in RMC

Monte Carlo (MC) burnup calculation method, implemented through coupling neutron transport and point depletion solvers, is widely used in design and analysis of nuclear reactor. Burnup calculation is generally solved by dividing reactor lifetime into steps and modeling geometry into numbers of burnup areas where neutron flux and one group effective cross sections are treated as constant during each burnup step. Such constant approximation for neutron flux and effective cross section will lead to obvious error unless using fairly short step. To yield accuracy and efficiency improvement, coupling schemes have been researched in series of MC codes. In this study, four coupling schemes, beginning of step approximation, predictor-corrector methods by correcting nuclide density and flux-cross section as well as high order predictor-corrector with sub-step method were researched and implemented in RMC. Verification and comparison were performed by adopting assembly problem from VERA international benchmark. Results illustrate that high order coupled with sub-step method is with notable accuracy compared to beginning of step approximation and traditional predictor-corrector, especially for calculation in which step length is fairly long.