Encoder-Decoder Approach to Predict Airport Operational Runway Configuration A case study for Amsterdam Schiphol airport

The runway configuration of an airport is the com- bination of runways that are active for arrivals and departures at any time. The runway configuration has a major influence on the capacity of the airport, taxiing times, the occupation of parking stands and taxiways, as well as on the management of traffic in the airspace surrounding the airport. The runway configuration of a given airport may change several times during the day, depending on the weather, air traffic demand and noise abatement rules, among other factors. This paper proposes an encoder-decoder model that is able to predict the future runway configuration sequence of an airport several hours upfront. In contrast to typical rule-based approaches, the proposed model is generic enough to be applied to any airport, since it only requires the past runway configuration history and the forecast traffic demand and weather in the prediction horizon. The performance of the model is assessed for the Amsterdam Schiphol Airport using three years of traffic, weather and runway use data.Peer ReviewedPostprint (published version

Assessment of the feasible CTA windows for efficient spacing with energy-neutral CDO

Continuous descent operations (CDO) with con- trolled times of arrival (CTA) at one or several metering fixes could enable environmentally friendly procedures at the same time that terminal airspace capacity is not compromised. This paper focuses on CTA updates once the descent has been already initiated, assessing the feasible CTA window (and associated fuel consumption) of CDO requiring neither thrust nor speed-brake usage along the whole descent (i.e. energy modulation through elevator control is used to achieve different times of arrival at the metering fixes). A multiphase optimal control problem is formulated and solved by means of numerical methods. The minimum and maximum times of arrival at the initial approach fix (IAF) and final approach point (FAP) of an hypothetical scenario are computed for an Airbus A320 descent and starting from a wide range of initial conditions. Results show CTA windows up to 4 minutes at the IAF and 70 seconds at the FAP. It has been also found that the feasible CTA window is affected by many factors, such as a previous CTA or the position of the top of descent. Moreover, minimum fuel trajectories almost correspond to those trajectories that minimise the time of arrival at the metering fix for the given initial conditionPeer ReviewedPostprint (published version

Finite element approximation of the viscoelastic flow problem: a non-residual based stabilized formulation

In this paper, a three-field finite element stabilized formulation for the incompressible viscoelastic fluid flow problem is tested numerically. Starting from a residual based formulation, a non-residual based one is designed, the benefits of which are highlighted in this work. Both formulations allow one to deal with the convective nature of the problem and to use equal interpolation for the problem unknowns View the MathML sources-u-p (deviatoric stress, velocity and pressure). Additionally, some results from the numerical analysis of the formulation are stated. Numerical examples are presented to show the robustness of the method, which include the classical 4: 1 planar contraction problem and the flow over a confined cylinder case, as well as a two-fluid formulation for the planar jet buckling problem.Peer ReviewedPostprint (author's final draft

A stabilized finite element method for the two-field and three-field Stokes eigenvalue problems

In this paper, the stabilized finite element approximation of the Stokes eigenvalue problems is considered for both the two-field (displacement-pressure) and the three-field (stress-displacement-pressure) formulations. The method presented is based on a subgrid scale concept, and depends on the approximation of the unresolvable scales of the continuous solution. In general, subgrid scale techniques consist in the addition of a residual based term to the basic Galerkin formulation. The application of a standard residual based stabilization method to a linear eigenvalue problem leads to a quadratic eigenvalue problem in discrete form which is physically inconvenient. As a distinguished feature of the present study, we take the space of the unresolved subscales orthogonal to the finite element space, which promises a remedy to the above mentioned complication. In essence, we put forward that only if the orthogonal projection is used, the residual is simplified and the use of term by term stabilization is allowed. Thus, we do not need to put the whole residual in the formulation, and the linear eigenproblem form is recovered properly. We prove that the method applied is convergent, and present the error estimates for the eigenvalues and the eigenfunctions. We report several numerical tests in order to illustrate that the theoretical results are validated

A stabilized finite element method for the two-field and three-field Stokes eigenvalue problems

In this paper, the stabilized finite element approximation of the Stokes eigenvalue problems is considered for both the two-field (displacement–pressure) and the three-field (stress–displacement–pressure) formulations. The method presented is based on a subgrid scale concept, and depends on the approximation of the unresolvable scales of the continuous solution. In general, subgrid scale techniques consist in the addition of a residual based term to the basic Galerkin formulation. The application of a standard residual based stabilization method to a linear eigenvalue problem leads to a quadratic eigenvalue problem in discrete form which is physically inconvenient. As a distinguished feature of the present study, we take the space of the unresolved subscales orthogonal to the finite element space, which promises a remedy to the above mentioned complication. In essence, we put forward that only if the orthogonal projection is used, the residual is simplified and the use of term by term stabilization is allowed. Thus, we do not need to put the whole residual in the formulation, and the linear eigenproblem form is recovered properly. We prove that the method applied is convergent, and present the error estimates for the eigenvalues and the eigenfunctions. We report several numerical tests in order to illustrate that the theoretical results are validated.Peer ReviewedPostprint (author's final draft

Comparison of some finite element methods for solving the diffusion-convection-reaction equation

In this paper we describe several finite element methods for solving the diffusion-convection-reaction equation. None of them is new, although the presentation is non-standard in an effort to emphasize the similarities and differences between them. In particular, it is shown that the classical SUPG method is very similar to an explicit version of the Characteristic-Galerkin method, whereas the Taylor-Galerkin method has a stabilization effect similar to a sub-grid scale model, which is un turn related to the introduction of bubbles functions

Finite element approximation of the hyperbolic wave equation in mixed form

The purpose of this paper is to present a finite element approximation of the scalar hyperbolic wave equation written in mixed form, that is, introducing an auxiliary vector field to transform the problem into a first-order problem in space and time. We explain why the standard Galerkin method is inappropriate to solve this problem, and propose as alternative a stabilized finite element method that can be cast in the variational multiscale framework. The unknown is split into its finite element component and a remainder, referred to as subscale. As original features of our approach, we consider the possibility of letting the subscales to be time dependent and orthogonal to the finite element space. The formulation depends on algorithmic parameters whose expression is proposed from a heuristic Fourier analysis

On stabilized finite element methods for linear systems of convection-diffusion-reaction equations

A stabilized finite element method for solving systems of convection-diffusion-reaction equations is studied in this paper. The method is based on the subgrid scale approach and an algebraic approximation to the subscales. After presenting the formulation of the method, it is analyzed how it behaves under changes of variables, showing that it relies on the law of change of the matrix of stabilization parameters associated to the method. An expression for this matrix is proposed for the case of general coupled systems of equations that is an extension of the expression proposed for a 1D model problem. Applications of the stabilization technique to the Stokes problem with convection and to the bending of Reissner-Mindlin plates are discussed next. The design of the matrix of stabilization parameters is based on the identification of the stability deficiencies of the standard Galerkin method applied to these two problems

Stabilized finite element approximation of transient incompressible flows using orthogonal subscales

In this paper we present a stabilized finite element method to solve the transient Navier–Stokes equations based on the decomposition of the unknowns into resolvable and subgrid scales. The latter are approximately accounted for, so as to end up with a stable finite element problem which, in particular, allows to deal with convection-dominated flows and the use of equal velocity–pressure interpolations. Three main issues are addressed. The first is a method to estimate the behavior of the stabilization parameters based on a Fourier analysis of the problem for the subscales. Secondly, the way to deal with transient problems discretized using a finite difference scheme is discussed. Finally, the treatment of the nonlinear term is also analyzed. A very important feature of this work is that the subgrid scales are taken as orthogonal to the finite element space. In the transient case, this simplifies considerably the numerical scheme

Comparison of some finite element methods for solving the diffusion-convection-reaction equation

In this paper we describe several finite element methods for solving the diffusion-convection-reaction equation. None of them is new, although the presentation is non-standard in an effort to emphasize the similarities and differences between them. In particular, it is shown that the classical SUPG method is very similar to an explicit version of the Characteristic-Galerkin method, whereas the Taylor-Galerkin method has a stabilization effect similar to a sub-grid scale model, which is un turn related to the introduction of bubbles functions