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We derive marginal conditions of optimality (i.e., Euler equations) for a general class of Dynamic Discrete Choice (DDC) structural models. These conditions can be used to estimate structural parameters in these models without having to solve for approximate value functions. This result extends to discrete choice models the GMM-Euler equation approach proposed by Hansen and Singleton (1982) for the estimation of dynamic continuous decision models. We first show that DDC models can be represented as models of continuous choice where the decision variable is a vector of choice probabilities. We then prove that the marginal conditions of optimality and the envelope conditions required to construct Euler equations are also satisfied in DDC models. The GMM estimation of these Euler equations avoids the curse of dimensionality associated to the computation of value functions and the explicit integration over the space of state variables. We present an empirical application and compare estimates using the GMM-Euler equations method with those from maximum likelihood and two-step methods.

The aim of the paper is to achieve textbook multigrid efficiency for some flow problems.

The steady incompressible Euler equations are decoupled into elliptic and hyperbolic subsystems. Numerous classical FAS‐MG algorithms are implemented and tested for convergence. A full multigrid algorithm that costs less than 10 work units (WUs) is sufficient to reduce the algebraic error below the discretization error. A new algorithm “NUVMGP” is introduced. A two‐step iterative procedure is adopted. First, given the pressure gradient, the convection equations are solved on the computational grid for the velocity components by performing one Gauss‐Seidel iteration ordered in the flow direction. second, a linear multigrid (MG) cycle for Poisson's equation is performed to update pressure values.

It is found that algorithm “NUVMGP‐FMG” requires less than 6 WU to attain the target solution. The convergence rates are independent on both the mesh size and the approximation order.

Lexicographic Gauss‐Seidel using downstream ordering is a good solver for the advection terms and provides excellent smoothing rates for relaxation. But it is complicated to maintain downstream ordering in case the flow directions change with location.

Although the scope of this work is limited to rectangular domains, finite difference schemes, and incompressible Euler equation, the same approaches can be extended for other flow problems. However, such relatively simple problems may provide deep understanding of the ideal convergence behavior of MG and accumulate experience to detect unacceptable performance and regain the optimal one.

An aerodynamic shape optimization algorithm is presented, which includes all aspects of the design process: parameterization, flow computation and optimization. The purpose of this paper is to show that the Class‐Shape‐Refinement‐Transformation method in combination with an Euler/adjoint solver provides an efficient and intuitive way of optimizing aircraft shapes.

The Class‐Shape‐Transformation method was used to parameterize the aircraft shape and the flow was computed using an in‐house Euler code. An adjoint solver implemented into the Euler code was used to compute the required gradients and a trust‐region reflective algorithm was employed to perform the actual optimization.

The results of two aerodynamic shape optimization test cases are presented. Both cases used a blended‐wing‐body reference geometry as their initial input. It was shown that using a two‐step approach, a considerable improvement of the lift‐to‐drag ratio in the order of 20‐30 per cent could be achieved. The work presented in this paper proves that the CSRT method is a very intuitive and effective way of parameterizating aircraft shapes. It was also shown that using an adjoint algorithm provides the computational efficiency necessary to perform true three‐dimensional shape optimization.

The novelty of the algorithm lies in the use of the Class‐Shape‐Refinement‐Transformation method for parameterization and its coupling to the Euler and adjoint codes.

A higher-order implicit shock-capturing scheme is presented for the Euler equations based on time linearization of the implicit flux vector rather than the residual vector.

The flux vector is linearized through a truncated Taylor-series expansion whose leading-order implicit term is an inner product of the flux Jacobian and the vector of differences between the current and previous time step values of conserved variables. The implicit conserved-variable difference vector is evaluated at cell faces by using the reconstructed states at the left and right sides of a cell face and projecting the difference between the left and right states onto the right eigenvectors. Flux linearization also facilitates the construction of implicit schemes with higher-order spatial accuracy (up to third order in the present study). To enhance the diagonal dominance of the coefficient matrix and thereby increase the implicitness of the scheme, wave strengths at cell faces are expressed as the inner product of the inverse of the right eigenvector matrix and the difference in the right and left reconstructed states at a cell face.

The accuracy of the implicit algorithm at Courant–Friedrichs–Lewy (CFL) numbers greater than unity is demonstrated for a number of test cases comprising one-dimensional (1-D) Sod’s shock tube, quasi 1-D steady flow through a converging-diverging nozzle, and two-dimensional (2-D) supersonic flow over a compression corner and an expansion corner.

The algorithm has the advantage that it does not entail spatial derivatives of flux Jacobian so that the implicit flux can be readily evaluated using Roe’s approximate Jacobian. As a result, this approach readily facilitates the construction of implicit schemes with high-order spatial accuracy such as Roe-MUSCL.

A novel finite-volume-based higher-order implicit shock-capturing scheme was developed that uses time linearization of fluxes at cell interfaces.

This study aims to decrease the aerodynamic drag of the body of revolution at supersonic speeds. Supersonic area rule is widely used in modern supersonic aircraft design. Further reduction of the aerodynamic drag is possible in the framework of Euler and Reynolds averaged Navier–Stokes (RANS) equations. Sears–Haack body of revolution shape variation, which decreased its aerodynamic drag in compressible inviscid and viscous gas flow at Mach number of 1.8 under constraint of the volume with lower bound equal to volume of initial body, was numerically investigated.

Calculations were carried out in two-dimensional axisymmetric mode in the framework of Euler and RANS with SST model with compressibility correction equations at structured multiblock meshes. Variation of the radius as function of the longitudinal coordinate was given as a polynomial third-order spline through five uniformly distributed points. Varied parameters were increments of the radius of the body at points that defined spline. Drag coefficient was selected as an objective function. Parameter combinations corresponding to the objective function minimum under volume constraint were obtained by mixed-integer sequential quadratic programming at second-order polynomial response surface and IOSO algorithm.

Improving variations make front part of the body become slightly blunted, transfer part of volume from front part of the body to back part and generate significant back face. In the framework of RANS, the best variation decreases aerodynamic drag by approximately 20 per cent in comparison with Sears–Haack body.

The results can be applied for the aerodynamic design of the bullets and projectiles. The second important application is knowledge of the significance of the difference between linearized slender body theory optimization results and optimization results obtained by modern computational fluid dynamics (CFD) optimization techniques.

Knowledge about the magnitude of the difference between linearized slender body theory optimization results and optimization results obtained by modern CFD optimization techniques can stimulate further research in related areas.

The optimization procedure and optimal shapes obtained in the present work are directly applicable to the design of small aerodynamic drag bodies.

The purpose of this paper is to investigate an active flow control technique called Shock Control Bump (SCB) for drag reduction using evolutionary algorithms.

A hierarchical genetic algorithm (HGA) consisting of multi‐fidelity models in three hierarchical topological layers is explored to speed up the design optimization process. The top layer consists of a single sub‐population operating on a precise model. On the middle layer, two sub‐populations operate on a model of intermediate accuracy. The bottom layer, consisting of four sub‐populations (two for each middle layer populations), operates on a coarse model. It is well‐known that genetic algorithms (GAs) are different from deterministic optimization tools in mimicking biological evolution based on Darwinian principle. In HGAs process, each population is handled by GA and the best genetic information obtained in the second or third layer migrates to the first or second layer for refinement.

The method was validated on a real life optimization problem consisting of two‐dimensional SCB design optimization installed on a natural laminar flow airfoil (RAE5243). Numerical results show that HGA is more efficient and achieves more drag reduction compared to a single population based GA.

Although the idea of HGA approach is not new, the novelty of this paper is to combine it with mesh/meshless methods and multi‐fidelity flow analyzers. To take the full benefit of using hierarchical topology, the following conditions are implemented: the first layer uses a precise meshless Euler solver with fine cloud of points, the second layer uses a hybrid mesh/meshless Euler solver with intermediate mesh/clouds of points, the third layer uses a less fine mesh with Euler solver to explore efficiently the search space with large mutation span.

A mathematical analysis of the time‐dependent multi‐dimensional Hydrodynamic model is performed to determine the well‐posed boundary conditions for semiconductor device simulation. The number of independent boundary conditions that need to be specified at electrical contacts of a semi‐conductor device are derived. Using the classical energy method, a mathematical relation among the physical parameters is established to define the well‐posed boundary conditions for the problem. Several possible sets of boundary conditions are given to illustrate the proper boundary conditions. Natural boundary conditions that can be specified are obtained from the boundary integrals of the weak‐form finite element formulations. An example is included to illustrate the importance of well‐posedness of the boundary conditions for device simulation.

We present results of a mathematical model for the gas flow in an internal combustion engine consisting of a single cylinder with an inlet and outlet pipe. In order to achieve optimal performance of the engine the dependence of the gas flow on physical parameters such as pipe dimensions and valve geometry need to be understood. A system of ordinary differential equations (in time t) with discontinuous right‐hand side describes the gas properties in the cylinder, whereas the gas flow in each pipe is modelled by the Euler equations, a system of hyperbolic partial differential equations. The explicit method of Euler and a TVD scheme are used for solving these equations. However, since the coupling of the pipe equations with the o.d.e. system in the cylinder on one side and atmospheric gas properties on the other appeared to be a main problem, we concentrate on appropriate coupling conditions. The numerical techniques involve discretization in space and time, and we present different methods of discrete coupling. As a main result we show that the various coupling methods lead to quite different numerical solutions. Therefore, a careful treatment of the coupling conditions is crucial.

MOST of the structural analysis problems that have resulted from the use of “thin‐walled” construction seem to fall into two general classes: Stress distribution and buckling. Even these classes cannot be entirely separated, as the stress distribution can be greatly affected by buckling phenomena. A thorough understanding of the general principles of buckling (or structural instability) is therefore essential for efficient and safe design of modern aircraft structures.

An implicit method for the solution of transonic flows modelled by the time‐dependent Euler equations is presented. The method is characterized by a robust linearization for first‐ and second‐order versions of Roe's flux‐difference splitting scheme, an implicit treatment of the boundary conditions and the implementation of an adaptive grid strategy for global efficiency. The performance of the method is investigated for the GAMM test circular‐arc bump configuration and for the RAE 2822 aerofoil.