Aircraft Noise Management

Several studies predict an increase up to 40% in traffic flights by the 2040. Airport noise control is a complicated procedure which creates an interesting blend of science, politics, and money. Accordingly, in many communities where airport noise is perceived as a significant problem, a noise control program is sometimes viewed as a continual process, rather than a discrete solution which will come to an end at some point in time.This work is an overview in the existing European low framework and the noise abatement procedure put in place to manage the aircraft noise.

DEVELOPMENT AND IMPLEMENTATION OF A TENTH-ORDER HYBRID BLOCK METHOD FOR SOLVING FIFTH-ORDER BOUNDARY VALUE PROBLEMS

A hybrid convergent method of tenth-order is presented in this work for directly solving fifth-order boundary value problems in ordinary differential equations. A unique direct block approach is obtained by combining multiple Finite Difference Formulas which are derived via the collocation technique. The proposed method is fully analyzed and the existence and uniqueness of the discrete solution is established. Different numerical examples are considered and the results are compared with those provided by existing works in the literature. The comparison shows the good performance of the present method over some cited works in the literature, confirming the competitiveness and superiority of the new numerical integrator.

Numerical Study of Inverse Source Problem for Internal Degenerate Parabolic Equation

This paper is devoted to numerical analysis of an inverse source problem in a degenerate parabolic equation. The aims of this work are to show the well-posedness of the discrete inverse problem and its convergence to the continuous one. For this, we reformulate first the encountered inverse problem to a regularized optimal control one. Then, we approximate our optimal control problem by finite element method and we show the existence of the discrete solution and its convergence to the continuous one. Finally, in order to confirm the efficiency of the proposed scheme, some numerical results are obtained using the augmented Lagrangian method.

WEB-Spline Finite Elements for the Approximation of Navier-Lamé System with CA,B Boundary Condition

The objective of this article is to discuss the existence and the uniqueness of a weighted extended B-spline- (WEB-spline-) based discrete solution for the 2D Navier-Lamé equation of linear elasticity with a different type of mixed boundary condition called CA,B boundary condition. Along with the usual weak mixed formulation, we give existence and uniqueness results for weak solution. Then, we illustrate the performance of Ritz–Galerkin schemes for a model problem and applications in linear elasticity. Finally, we discuss several implementation aspects. The numerical tests confirm that, due to the new integration routines, the weighted B-spline solvers have become considerably more efficient.

Enhanced positive vertex-centered finite volume scheme for anisotropic convection-diffusion equations

This article is about the development and the analysis of an enhanced positive control volume finite element scheme for degenerate convection-diffusion type problems. The proposed scheme involves only vertex unknowns and features anisotropic fields. The novelty of the approach is to devise a reliable upwind approximation with respect to flux-like functions for the elliptic term. Then, it is shown that the discrete solution remains nonnegative. Under general assumptions on the data and the mesh, the convergence of the numerical scheme is established owing to a recent compactness argument. The efficiency and stability of the methodology are numerically illustrated for different anisotropic ratios and nonlinearities.

Designing Self Supported SLM Structures via Topology Optimization

The potential of Additive Manufacturing (AM) is high, with a whole new set of manufactured parts with unseen complexity being offered. However, the process has limitations, and for the sake of economic competitiveness, these should also be considered. Therefore, a computational methodology, capable of including the referenced limitations and providing initial solid designs for Selective Laser Melting (SLM) is the subject of the present work. The combination of Topology Optimization (TO) with the simplified fabrication model is the selected methodology. Its formulation, implementation, and integration on the classic TO algorithm is briefly discussed, being capable of addressing the minimum feature size and the overhang constraint limitations. Moreover, the performance and numerical stability of the methodology is evaluated, and numerical variables, such as the accuracy of structural equilibrium equations and the material interpolation model, are considered. A comparative study between these variables is presented. The paper then proposes an enhanced version of the selected methodology, with a better convergence towards a discrete solution.

A Second-Order Uniformly Stable Explicit Asymmetric Discretization Method for One-Dimensional Fractional Diffusion Equations

Using the asymmetric discretization technique, an explicit finite difference scheme is constructed for one-dimensional spatial fractional diffusion equations (FDEs). The spatial fractional derivative is approximated by the weighted and shifted Grünwald difference operator. The scheme can be solved explicitly by calculating unknowns in the different nodal-point sequences at the odd time-step and the even time-step. The uniform stability is proven and the error between the discrete solution and analytical solution is theoretically estimated. Numerical examples are given to verify theoretical analysis.

An easily computable error estimator in space and time for the wave equation

We propose a cheaper version of a posteriori error estimator from Gorynina et al. (Numer. Anal. (2017)) for the linear second-order wave equation discretized by the Newmark scheme in time and by the finite element method in space. The new estimator preserves all the properties of the previous one (reliability, optimality on smooth solutions and quasi-uniform meshes) but no longer requires an extra computation of the Laplacian of the discrete solution on each time step.