Introduction to linear and nonlinear programming

This article shows how the evolution of multi-commodity traffic flows over complex networks can be predicted over time, based on a simple macroscopic computer representation of traffic flow that is consistent with the kinematic wave theory under all traffic conditions. The method does not use ad hoc procedures to treat special situations. After a brief review of the basic model for one link, the article describes how three-legged junctions can be modeled. It then introduces a numerical procedure for networks, assuming that a time-varying origin-destination (O-D) table is given and that the proportion of turns at every junction is known. These assumptions are reasonable for numerical analysis of disaster evacuation plans. The results are then extended to the case where, instead of the turning proportions, the best routes to each destination from every junction are known at all times. For technical reasons explained in the text, the procedure is more complicated in this case, requiring more computer memory and more time for execution. The effort is estimated to be about an order of magnitude greater than for the static traffic assignment problem on a network of the same size. The procedure is ideally suited for parallel computing. It is hoped that the results in the article will lead to more realistic models of freeway flow, disaster evacuations and dynamic traffic assignment for the evening commute.

The cell transmission model, part ii: network traffic

: This research organizes, presents, and analyzes contemporary Multiobjective Evolutionary Algorithm (MOEA) research and associated Multiobjective Optimization Problems (MOPs). Using a consistent MOEA terminology and notation, each cited MOEAs' key factors are presented in tabular form for ease of MOEA identification and selection. A detailed quantitative and qualitative MOEA analysis is presented, providing a basis for conclusions about various MOEA-related issues. The traditional notion of building blocks is extended to the MOP domain in an effort to develop more effective and efficient MOEAs. Additionally, the MOEA community's limited test suites contain various functions whose origins and rationale for use are often unknown. Thus, using general test suite guidelines appropriate MOEA test function suites are substantiated and generated. An experimental methodology incorporating a solution database and appropriate metrics is offered as a proposed evaluation framework allowing absolute comparisons of specific MOEA approaches. Taken together, this document's classifications, analyses, and new innovations present a complete, contemporary view of current MOEA "state of the art" and possible future research. Researchers with basic EA knowledge may also use part of it as a largely self-contained introduction to MOEAs.

Multiobjective evolutionary algorithms: classifications, analyses, and new innovations

Aircraft wings are a compromise that allows the aircraft to fly at a range of flight conditions, but the performance at each condition is sub-optimal. The ability of a wing surface to change its geometry during flight has interested researchers and designers over the years as this reduces the design compromises required. Morphing is the short form for metamorphose; however, there is neither an exact definition nor an agreement between the researchers about the type or the extent of the geometrical changes necessary to qualify an aircraft for the title ‘shape morphing.’ Geometrical parameters that can be affected by morphing solutions can be categorized into: planform alteration (span, sweep, and chord), out-of-plane transformation (twist, dihedral/gull, and span-wise bending), and airfoil adjustment (camber and thickness). Changing the wing shape or geometry is not new. Historically, morphing solutions always led to penalties in terms of cost, complexity, or weight, although in certain circumstances, thes...

A Review of Morphing Aircraft

An efficient ghost-cell immersed boundary method (GCIBM) for simulating turbulent flows in complex geometries is presented. A boundary condition is enforced through a ghost cell method. The reconstruction procedure allows systematic development of numerical schemes for treating the immersed boundary while preserving the overall second-order accuracy of the base solver. Both Dirichlet and Neumann boundary conditions can be treated. The current ghost cell treatment is both suitable for staggered and non-staggered Cartesian grids. The accuracy of the current method is validated using flow past a circular cylinder and large eddy simulation of turbulent flow over a wavy surface. Numerical results are compared with experimental data and boundary-fitted grid results. The method is further extended to an existing ocean model (MITGCM) to simulate geophysical flow over a three-dimensional bump. The method is easily implemented as evidenced by our use of several existing codes.

A Ghost-Cell Immersed Boundary Method for Flow in Complex Geometry

A review of recent advances in the use of surface integral methods in Computational AeroAcoustics (CAA) for the extension of near-field CFD results to the acoustic far-field is given. These integral formulations (i.e. Kirchhoff's method, permeable (porous) surface FfowcsWilliams Hawkings (FW-H) equation) allow the radiating sound to be evaluated based on quantities on an arbitrary control surface if the wave equation is assumed outside. Thus only surface integrals are needed for the calculation of the far-field sound, instead of the volume integrals required by the traditional acoustic analogy method (i.e. Lighthill, rigid body FW-H equation). A numerical CFD method is used for the evaluation of the flow-field solution in the near field and thus on the control surface. Diffusion and dispersion errors associated with wave propagation in the far-field are avoided. The surface integrals and the first derivatives needed can be easily evaluated from the near-field CFD data. Both methods can be extended in orde...

https://engineering.purdue.edu/~lyrintzi/JAAfinal.pdf

Surface integral methods in computational aeroacoustics—From the (CFD) near-field to the (Acoustic) far-field

A comprehensive review of the use of Kirchhoff's method in computational aeroacoustics is given Kirchhoff's integral formulation allows radiating sound to be evaluated based on quantities on an arbitrary control surface S if the wave equation is assumed outside The control surface S is assumed to include all the nonlinear flow effects and noise sources Thus only surface integrals are needed for the calculation of the far-field sound A numerical CFD method can be used for the evaluation of the flow-field solution in the near-field and thus on surface S Kirchhoff's integral formulation has been intended to an arbitrary, moving, deformable piecewise-continuous surface The available Kirchhoff formulations are reviewed and various aeroacoustic applications are given The relative merits of Kirchhoff's method are also discussed

Review: the use of Kirchhoff's method in computational aeroacoustics

This study is focused on developing a Computational Aeroacoustics (CAA) methodology that couples the near field unsteady flow field data computed by a 3-D Large Eddy Simulation (LES) code with various integral acoustic formulations for the far field noise prediction of turbulent jets. The LES code employs state-of-the-art numerical schemes and a localized version of the dynamic Smagorinsky subgrid-scale (SGS) model. The code also has the capability to turn off the SGS model and treat the spatial filter that is needed for numerical stability as an implicit SGS model. Noise computations performed for a Mach 0.9, Reynolds number 400,000 jet using various integral acoustic results are presented and the results are compared against each other as well with those from experiments at similar flow conditions. Our results show that the surface integral acoustics methods (Kirchhoff and Ffowcs Williams - Hawkings) give similar results to the volume integral method (Lighthill's acoustic analogy) at a much lower cost. To the best of our knowledge, Lighthill's acoustic analogy is applied to a Reynolds number 400,000 jet at Mach 0.9 for the first time in this study. The distribution of Lighthill sources that radiate noise in the direction of various observer locations is evaluated. A source decomposition shows significant cancellations among the individual components of the Lighthill source.

https://engineering.purdue.edu/~lyrintzi/Reno04Ali.pdf

Coupling of integral acoustics methods with LES for jet noise prediction

This paper investigates advanced continuum models for describing traffic dynamics at congested flows. First, the existing high-order models are reviwed and discussed, and a new formulation is proposed which does not require the use of an equilibrium speed-density relationship. (A model is of high-order when it includes both mass and momentum conservation.) Traffic friction at interrupted flows and changing geometries is also addressed through the use of a viscosity term. The model is then discretized through two alternative numerical schemes to examine the effectiveness of the implementation. Stability analysis is performed to set up numerical limits of the model parameters. Finally, in two test cases with congested and uncongested field data, the new model is compared with the existing models; this comparison suggests that the proposed mode is more accurate and computationally more efficient.

Continuum modelling of traffic dynamics for congested freeways

of the unresolved scales on the resolved scales. A computational grid consisting of 12 million points was used in the present simulation. Mean flow results obtained in our simulation are found to be in excellent agreement with the available experimental data of jets at similar flow conditions. Furthermore, the near field data provided by LES is coupled with the Ffowcs Williams-Hawkings method to compute the far field noise. Far field aeroacoustics results are also presented and comparisons are made with another computational study.

Anastasios S. Lyrintzis

Papers

Surface integral methods in computational aeroacoustics—From the (CFD) near-field to the (Acoustic) far-field

Review: the use of Kirchhoff's method in computational aeroacoustics

Coupling of integral acoustics methods with LES for jet noise prediction

Continuum modelling of traffic dynamics for congested freeways

3-D large eddy simulation for jet aeroacoustics