Multi-Objective and Multi-Phase 4D Trajectory Optimization for Climate Mitigation-Oriented Flight Planning

Aviation contribution to global warming and anthropogenic climate change is increasing every year. To reverse this trend, it is crucial to identify greener alternatives to current aviation technologies and paradigms. Research in aircraft operations can provide a swift response to new environmental requirements, being easier to exploit on current fleets. This paper presents the development of a multi-objective and multi-phase 4D trajectory optimization tool to be integrated within a Flight Management System of a commercial aircraft capable of performing 4D trajectory tracking in a Free Route Airspace context. The optimization algorithm is based on a Chebyshev pseudospectral method, adapted to perform a multi-objective optimization with the two objectives being the Direct Operating Cost and the climate cost of a climb-cruise-descent trajectory. The climate cost function applies the Global Warming Potential metric to derive a comprehensive cost index that includes the climate forcing produced by CO2 and non-CO2 emissions, and by the formation of aircraft-induced clouds. The output of the optimization tool is a set of Pareto-optimal 4D trajectories among which the aircraft operator can choose the best solution that satisfies both its economic and environmental goals.

Hermite-Chebyshev pseudospectral method for inhomogeneous superconducting strip problems and magnetic flux pump modeling

Numerical simulation of superconducting devices is a powerful tool for understanding the principles of their work and improving their design. Usually, such simulations are based on a finite element method but, recently, a different approach, based on the spectral technique, has been presented for very efficient solution of several applied superconductivity problems described by one-dimensional integro-differential equations or a system of such equations. Here we propose a new pseudospectral method for two-dimensional magnetization and transport current superconducting strip problems with an arbitrary current-voltage relation, spatially inhomogeneous strips, and strips in a nonuniform applied field. The method is based on the bivariate expansions in Chebyshev polynomials and Hermite functions. It can be used for numerical modeling magnetic flux pumps of different types and investigating AC losses in coated conductors with local defects. Using a realistic two-dimensional version of the superconducting dynamo benchmark problem as an example, we showed that our new method is a competitive alternative to finite element methods.

Numerical Analysis of the Fractional-Order Nonlinear System of Volterra Integro-Differential Equations

This paper presents the nonlinear systems of Volterra-type fractional integro-differential equation solutions through a Chebyshev pseudospectral method. The proposed method is based on the Caputo fractional derivative. The results that we get show the accuracy and reliability of the present method. Different nonlinear systems have been solved; the solutions that we get are compared with other methods and the exact solution. Also, from the presented figures, it is easy to conclude that the CPM error converges quickly as compared to other methods. Comparing the exact solution and other techniques reveals that the Chebyshev pseudospectral method has a higher degree of accuracy and converges quickly towards the exact solution. Moreover, it is easy to implement the suggested method for solving fractional-order linear and nonlinear physical problems related to science and engineering.

The onset of magnetic nanofluid convection because of selective absorption of radiation

This article reports a linear stability analysis of the onset of convection stimulated by selective absorption of radiation in a horizontal layer of magnetic nanofluid (MNF) under the impact of an external magnetic field. The Chebyshev pseudospectral method is utilized to obtain the numerical solution for water-based magnetic nanofluids (MNFs). The confining boundaries of the magnetic nanofluid layer are considered to be rigid–rigid, rigid–free, and free–free. The results are derived for two different conditions, viz., when the system is heated from the below and when the system is heated from the above. It is observed that an increase in the value of the Langevin parameter , diffusivity ratio and a decrease in the value of nanofluid Lewis number , the parameter which represents the impact of selective absorption of radiation and modified diffusivity ratio delays the onset of MNF convection for both the two configurations. Moreover, as the value of concentration Rayleigh number increases, the convection commences easily when the system is heated from the below, whereas the onset of MNF convection gets delayed as the system is heated from the above.

On successive linearization method for differential equations with nonlinear conditions

This paper presents a new technique for solving linear and nonlinear boundary value problems subject to linear or nonlinear conditions. The technique is based on the blending of the Chebyshev pseudospectral method. The rapid convergence and effectiveness are verified by several linear and nonlinear examples, and results are compared with the exact solutions. Our results show a remarkable improvement in the convergence of the results when compared with exact solutions.

Legendre-Chebyshev pseudo-spectral method for the diffusion equation with non-classical boundary conditions

The present paper is devoted to the numerical approximation for the diffusion equation subject to non-local boundary conditions. For the space discretization, we apply the Legendre-Chebyshev pseudospectral method, so that, the problem under consideration is reduced to a system of ODEs which can be solved by the second order Crank-Nicolson schema. Optimal error estimates for the semi-discrete scheme are derived in L2-norm. Numerical tests are included to demonstrate the effectiveness of the proposed method.